DC Pandey Solutions (JEE Main): Electrostatic- 1 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
Subjective Questions 
  Note : You can take approximations in the answers. 
  Coulomb's Law 
Q 1.  A certain charge Q is divided into two parts q and Q - q, which are then separated by a certain 
distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two 
charges? 
Q 2.  Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible 
magnitude of the electric force acting on each charge? 
Q 3.  An ?-particle is the nucleus of a helium atom. It has a mass m = 6.64 × 10
-27
 kg and a charge q - + 
2e = 3.2 × 10
-19
 C. Compare the force of the electric repulsion between two ?-particles with the 
force of gravitational attraction between them. 
Q 4.  Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of 
0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the 
spheres. When the wire is removed, the spheres repel each other with an electrostatic force of 
0.0360 N. What were the initial charges on the spheres? 
Q 5.  Point charges q
1
 and q
2
 lie on the x-axis at points x = - a and x = + a respectively. 
(a) How must q
1
 and q
2
 be related for the net electrostatic force on point charge + Q, placed at x = 
+ a/2, to be zero? 
  (b) With the same point charge +Q now placed at x = + 3a/2. 
Q 6.  Two particles (free to move) with charges +q and +4q are a distance L apart. A third charge is 
placed so that the entire system is in equilibrium. 
  (a) Find the location, magnitude and sign of the third charge. 
  (b) Show that the equilibrium is unstable. 
Q 7.  Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of 
radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a 
distance R apart (figure). Determine the charge on each bead.  
 
Q 8.  Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a 
length of l = 20cm. What charges should be imparted to the balls for each thread to form an angle 
of ? = 30?
 
with the vertical? 
  Electric Field 
Q 9.  Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The 
distance of each corner from the centre is a. Find the electric field at the centre of the pentagon. 
Q 10.  Three charges, each equal to q, are placed at the three corners of a square of side a. Find the 
electric field at fourth corner. 
Page 2


Exercises 
For JEE Main 
Subjective Questions 
  Note : You can take approximations in the answers. 
  Coulomb's Law 
Q 1.  A certain charge Q is divided into two parts q and Q - q, which are then separated by a certain 
distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two 
charges? 
Q 2.  Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible 
magnitude of the electric force acting on each charge? 
Q 3.  An ?-particle is the nucleus of a helium atom. It has a mass m = 6.64 × 10
-27
 kg and a charge q - + 
2e = 3.2 × 10
-19
 C. Compare the force of the electric repulsion between two ?-particles with the 
force of gravitational attraction between them. 
Q 4.  Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of 
0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the 
spheres. When the wire is removed, the spheres repel each other with an electrostatic force of 
0.0360 N. What were the initial charges on the spheres? 
Q 5.  Point charges q
1
 and q
2
 lie on the x-axis at points x = - a and x = + a respectively. 
(a) How must q
1
 and q
2
 be related for the net electrostatic force on point charge + Q, placed at x = 
+ a/2, to be zero? 
  (b) With the same point charge +Q now placed at x = + 3a/2. 
Q 6.  Two particles (free to move) with charges +q and +4q are a distance L apart. A third charge is 
placed so that the entire system is in equilibrium. 
  (a) Find the location, magnitude and sign of the third charge. 
  (b) Show that the equilibrium is unstable. 
Q 7.  Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of 
radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a 
distance R apart (figure). Determine the charge on each bead.  
 
Q 8.  Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a 
length of l = 20cm. What charges should be imparted to the balls for each thread to form an angle 
of ? = 30?
 
with the vertical? 
  Electric Field 
Q 9.  Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The 
distance of each corner from the centre is a. Find the electric field at the centre of the pentagon. 
Q 10.  Three charges, each equal to q, are placed at the three corners of a square of side a. Find the 
electric field at fourth corner. 
Q 11.  A point charge q = -8.0 nC is located at the origin. Find the electric field vector at the point x = 1.2 
m, y = - 1.6 m. 
Q 12.  Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear 
charge density is ?. 
Q 13.  Find the electric field at a point P on the perpendicular bisector of a unifromly charged rod. The 
length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a. 
Q 14.  Find the direction of electric field at point P for the charge distribution as shown in figure. 
  (a)    (b)    (c)  
Q 15.  A clock face has charges - q, - 2q, - 3q,.. . - 12q fixed at the position of the corresponding 
numerals on the dial. The clock hands do not disturb the net field due to point charges. At what 
time does the hour hand point in the direction of the electric field at the centre of the dial. 
  Electric Forces 
Q 16.  An electron with a speed of 5.00 × 10
8
 cm/s enters an electric field of magnitude 1.00 × 10
3
 N/C, 
travelling along the field lines in the direction that retards its motion. 
(a) How far will the electron travel in the field before stopping momentarily and 
(b) How much time will have elapsed? 
(c) If the region with the electric field is only 8.00 mm long (too short from the electron to stop 
with in it), what fraction of the electron's initial kinetic energy will be lost in that region? 
Q 17.  A charged particle of mass m = 1 kg and charge q = 2 ?C is thrown from a horizontal ground at an 
angle ? = 45? with the speed 25 m/s. In space a horizontal electric field E = 2 × 10
7
 V/m exist in 
the direction of motion. Find the range on horizontal ground of the projectile thrown. Take g = 10 
m/s
2
. 
Q 18.  Protons are projected with an initial speed v
i
 = 9.55 × 10
3
 m/s into a region where a uniform 
electric field
ˆ
E ( 720j)N/ C ??
?
 
is present, as shown in figure. The protons are to hit a target that 
lies at a horizontal distance of 1.27 mm from the point where the protons are launched. Find : 
(a) the two projection angles ?
 
that result in a hit and 
(b) the total time of flight for each trajectory.  
 
Q 19.  At some instant the velocity components of an electron moving between two charged parallel 
plates are v
x
 = 1.5 × 10
5
 m/s and v
y
 = 3.0 × 10
6
 m/s. Suppose that the electric field between the 
plates is given by 
   
ˆ
E (120N/ C)j ?
?
 
(a) What is the acceleration of the electron? 
Page 3


Exercises 
For JEE Main 
Subjective Questions 
  Note : You can take approximations in the answers. 
  Coulomb's Law 
Q 1.  A certain charge Q is divided into two parts q and Q - q, which are then separated by a certain 
distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two 
charges? 
Q 2.  Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible 
magnitude of the electric force acting on each charge? 
Q 3.  An ?-particle is the nucleus of a helium atom. It has a mass m = 6.64 × 10
-27
 kg and a charge q - + 
2e = 3.2 × 10
-19
 C. Compare the force of the electric repulsion between two ?-particles with the 
force of gravitational attraction between them. 
Q 4.  Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of 
0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the 
spheres. When the wire is removed, the spheres repel each other with an electrostatic force of 
0.0360 N. What were the initial charges on the spheres? 
Q 5.  Point charges q
1
 and q
2
 lie on the x-axis at points x = - a and x = + a respectively. 
(a) How must q
1
 and q
2
 be related for the net electrostatic force on point charge + Q, placed at x = 
+ a/2, to be zero? 
  (b) With the same point charge +Q now placed at x = + 3a/2. 
Q 6.  Two particles (free to move) with charges +q and +4q are a distance L apart. A third charge is 
placed so that the entire system is in equilibrium. 
  (a) Find the location, magnitude and sign of the third charge. 
  (b) Show that the equilibrium is unstable. 
Q 7.  Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of 
radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a 
distance R apart (figure). Determine the charge on each bead.  
 
Q 8.  Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a 
length of l = 20cm. What charges should be imparted to the balls for each thread to form an angle 
of ? = 30?
 
with the vertical? 
  Electric Field 
Q 9.  Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The 
distance of each corner from the centre is a. Find the electric field at the centre of the pentagon. 
Q 10.  Three charges, each equal to q, are placed at the three corners of a square of side a. Find the 
electric field at fourth corner. 
Q 11.  A point charge q = -8.0 nC is located at the origin. Find the electric field vector at the point x = 1.2 
m, y = - 1.6 m. 
Q 12.  Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear 
charge density is ?. 
Q 13.  Find the electric field at a point P on the perpendicular bisector of a unifromly charged rod. The 
length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a. 
Q 14.  Find the direction of electric field at point P for the charge distribution as shown in figure. 
  (a)    (b)    (c)  
Q 15.  A clock face has charges - q, - 2q, - 3q,.. . - 12q fixed at the position of the corresponding 
numerals on the dial. The clock hands do not disturb the net field due to point charges. At what 
time does the hour hand point in the direction of the electric field at the centre of the dial. 
  Electric Forces 
Q 16.  An electron with a speed of 5.00 × 10
8
 cm/s enters an electric field of magnitude 1.00 × 10
3
 N/C, 
travelling along the field lines in the direction that retards its motion. 
(a) How far will the electron travel in the field before stopping momentarily and 
(b) How much time will have elapsed? 
(c) If the region with the electric field is only 8.00 mm long (too short from the electron to stop 
with in it), what fraction of the electron's initial kinetic energy will be lost in that region? 
Q 17.  A charged particle of mass m = 1 kg and charge q = 2 ?C is thrown from a horizontal ground at an 
angle ? = 45? with the speed 25 m/s. In space a horizontal electric field E = 2 × 10
7
 V/m exist in 
the direction of motion. Find the range on horizontal ground of the projectile thrown. Take g = 10 
m/s
2
. 
Q 18.  Protons are projected with an initial speed v
i
 = 9.55 × 10
3
 m/s into a region where a uniform 
electric field
ˆ
E ( 720j)N/ C ??
?
 
is present, as shown in figure. The protons are to hit a target that 
lies at a horizontal distance of 1.27 mm from the point where the protons are launched. Find : 
(a) the two projection angles ?
 
that result in a hit and 
(b) the total time of flight for each trajectory.  
 
Q 19.  At some instant the velocity components of an electron moving between two charged parallel 
plates are v
x
 = 1.5 × 10
5
 m/s and v
y
 = 3.0 × 10
6
 m/s. Suppose that the electric field between the 
plates is given by 
   
ˆ
E (120N/ C)j ?
?
 
(a) What is the acceleration of the electron? 
(b) What will be the velocity of the electron after its x-coordinate has changed by 2.0 cm? 
Electric Potential and Electric Potential Energy 
Q 20.  A point charge q
1
 = +2 ?C is placed at the origin of co-ordinates. A second charge, q
2
 = - 3 ?C, is 
placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute 
potential be zero?  
 
Q 21.  A charge Q is spread uniformly in the form of a line charge density 
Q
3a
?? on the sides of an 
equilateral triangle of perimeter 3a. Calculate the potential at the centriod C of the triangle. 
Q 22.  A uniform electric field of magnitude 250 V/m is directed in the positive x-direction. A + 12 ?C 
charge moves from the origin to the point (x, y) = (20.0cm, 5.0cm). 
(a) What was the change in the potential energy of this charge? 
(b) Through what potential difference did the charge move? 
Q 23.  A small particle has charge -5.00 ?C and mass 2.00 × 10
-4
 Kg. it moves from points, where the 
electric potential is V
A
 =+ 200 V, to point B, where the electric potential is V
B
 = + 800 V. The 
electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. 
What is its speed at point B ? Is it moving faster or slower at B than at A ? Explain. 
Q 24.  A plastic rod has been formed into a circle of radius R. It has a positive charge +Q uniformly 
distributed along one-quarter of its circumference and a negative charge of - 6Q uniformly 
distributed along the rest of the circumference (figure). With V = 0 at infinity, what is the electric 
potential 
(a) at the centre C of the circle and 
(b) at point P, which is on the central axis of the circle at distance z from the centre? 
 
Q 25.  A point charge q
1
 = + 2.40 ?C is held stationary at the origin. A second point charge q
2
 = -4.30 ?C 
moves from the point x = 0.150m, y = 0 to the point x = 0.250 m, y = 0.250 m. How much work is 
done by the electric force on q
2
? 
Q 26.  A point charge q
1
 = 4.00 nC is placed at the origin, and a second point charge q
2
= - 3.00 nC is 
placed on the x-axis at x = + 20.0cm A third point charge q
3
 = 2.00 nC is placed on the x-axis 
between q
1
 and q
2
. (Take as zero the potential energy of the three charges when they are infinitely 
far apart). 
(a) What is the potential energy of the system of the three charges if q
3
 is placed at x= +10.0cm ? 
(b) Where should q
3
 be placed to make the potential energy of the system equal to zero? 
Page 4


Exercises 
For JEE Main 
Subjective Questions 
  Note : You can take approximations in the answers. 
  Coulomb's Law 
Q 1.  A certain charge Q is divided into two parts q and Q - q, which are then separated by a certain 
distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two 
charges? 
Q 2.  Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible 
magnitude of the electric force acting on each charge? 
Q 3.  An ?-particle is the nucleus of a helium atom. It has a mass m = 6.64 × 10
-27
 kg and a charge q - + 
2e = 3.2 × 10
-19
 C. Compare the force of the electric repulsion between two ?-particles with the 
force of gravitational attraction between them. 
Q 4.  Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of 
0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the 
spheres. When the wire is removed, the spheres repel each other with an electrostatic force of 
0.0360 N. What were the initial charges on the spheres? 
Q 5.  Point charges q
1
 and q
2
 lie on the x-axis at points x = - a and x = + a respectively. 
(a) How must q
1
 and q
2
 be related for the net electrostatic force on point charge + Q, placed at x = 
+ a/2, to be zero? 
  (b) With the same point charge +Q now placed at x = + 3a/2. 
Q 6.  Two particles (free to move) with charges +q and +4q are a distance L apart. A third charge is 
placed so that the entire system is in equilibrium. 
  (a) Find the location, magnitude and sign of the third charge. 
  (b) Show that the equilibrium is unstable. 
Q 7.  Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of 
radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a 
distance R apart (figure). Determine the charge on each bead.  
 
Q 8.  Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a 
length of l = 20cm. What charges should be imparted to the balls for each thread to form an angle 
of ? = 30?
 
with the vertical? 
  Electric Field 
Q 9.  Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The 
distance of each corner from the centre is a. Find the electric field at the centre of the pentagon. 
Q 10.  Three charges, each equal to q, are placed at the three corners of a square of side a. Find the 
electric field at fourth corner. 
Q 11.  A point charge q = -8.0 nC is located at the origin. Find the electric field vector at the point x = 1.2 
m, y = - 1.6 m. 
Q 12.  Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear 
charge density is ?. 
Q 13.  Find the electric field at a point P on the perpendicular bisector of a unifromly charged rod. The 
length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a. 
Q 14.  Find the direction of electric field at point P for the charge distribution as shown in figure. 
  (a)    (b)    (c)  
Q 15.  A clock face has charges - q, - 2q, - 3q,.. . - 12q fixed at the position of the corresponding 
numerals on the dial. The clock hands do not disturb the net field due to point charges. At what 
time does the hour hand point in the direction of the electric field at the centre of the dial. 
  Electric Forces 
Q 16.  An electron with a speed of 5.00 × 10
8
 cm/s enters an electric field of magnitude 1.00 × 10
3
 N/C, 
travelling along the field lines in the direction that retards its motion. 
(a) How far will the electron travel in the field before stopping momentarily and 
(b) How much time will have elapsed? 
(c) If the region with the electric field is only 8.00 mm long (too short from the electron to stop 
with in it), what fraction of the electron's initial kinetic energy will be lost in that region? 
Q 17.  A charged particle of mass m = 1 kg and charge q = 2 ?C is thrown from a horizontal ground at an 
angle ? = 45? with the speed 25 m/s. In space a horizontal electric field E = 2 × 10
7
 V/m exist in 
the direction of motion. Find the range on horizontal ground of the projectile thrown. Take g = 10 
m/s
2
. 
Q 18.  Protons are projected with an initial speed v
i
 = 9.55 × 10
3
 m/s into a region where a uniform 
electric field
ˆ
E ( 720j)N/ C ??
?
 
is present, as shown in figure. The protons are to hit a target that 
lies at a horizontal distance of 1.27 mm from the point where the protons are launched. Find : 
(a) the two projection angles ?
 
that result in a hit and 
(b) the total time of flight for each trajectory.  
 
Q 19.  At some instant the velocity components of an electron moving between two charged parallel 
plates are v
x
 = 1.5 × 10
5
 m/s and v
y
 = 3.0 × 10
6
 m/s. Suppose that the electric field between the 
plates is given by 
   
ˆ
E (120N/ C)j ?
?
 
(a) What is the acceleration of the electron? 
(b) What will be the velocity of the electron after its x-coordinate has changed by 2.0 cm? 
Electric Potential and Electric Potential Energy 
Q 20.  A point charge q
1
 = +2 ?C is placed at the origin of co-ordinates. A second charge, q
2
 = - 3 ?C, is 
placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute 
potential be zero?  
 
Q 21.  A charge Q is spread uniformly in the form of a line charge density 
Q
3a
?? on the sides of an 
equilateral triangle of perimeter 3a. Calculate the potential at the centriod C of the triangle. 
Q 22.  A uniform electric field of magnitude 250 V/m is directed in the positive x-direction. A + 12 ?C 
charge moves from the origin to the point (x, y) = (20.0cm, 5.0cm). 
(a) What was the change in the potential energy of this charge? 
(b) Through what potential difference did the charge move? 
Q 23.  A small particle has charge -5.00 ?C and mass 2.00 × 10
-4
 Kg. it moves from points, where the 
electric potential is V
A
 =+ 200 V, to point B, where the electric potential is V
B
 = + 800 V. The 
electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. 
What is its speed at point B ? Is it moving faster or slower at B than at A ? Explain. 
Q 24.  A plastic rod has been formed into a circle of radius R. It has a positive charge +Q uniformly 
distributed along one-quarter of its circumference and a negative charge of - 6Q uniformly 
distributed along the rest of the circumference (figure). With V = 0 at infinity, what is the electric 
potential 
(a) at the centre C of the circle and 
(b) at point P, which is on the central axis of the circle at distance z from the centre? 
 
Q 25.  A point charge q
1
 = + 2.40 ?C is held stationary at the origin. A second point charge q
2
 = -4.30 ?C 
moves from the point x = 0.150m, y = 0 to the point x = 0.250 m, y = 0.250 m. How much work is 
done by the electric force on q
2
? 
Q 26.  A point charge q
1
 = 4.00 nC is placed at the origin, and a second point charge q
2
= - 3.00 nC is 
placed on the x-axis at x = + 20.0cm A third point charge q
3
 = 2.00 nC is placed on the x-axis 
between q
1
 and q
2
. (Take as zero the potential energy of the three charges when they are infinitely 
far apart). 
(a) What is the potential energy of the system of the three charges if q
3
 is placed at x= +10.0cm ? 
(b) Where should q
3
 be placed to make the potential energy of the system equal to zero? 
Q 27.  Three point charges, which initially are infinitely far apart, are placed at the corners of an 
equilateral triangle with sides d. Two of the point charges are identical and have charge q. If zero 
net work is required to place the three charges at the corners of the triangles, what must the value 
of the third charge be? 
  Relation between Electric Field and Potential 
Q 28.  The electric field in a certain region is given by 
ˆˆ
E 5i 3jkV/ m ??
?
.
 
Find the difference in potential 
V
B
 - V
A
 . If A is at the origin and point B is at 
(a) (0, 0, 5) m,   (b) (4,0,3)m. 
Q 29.  In a certain region of space, the electric field is along +y direction and has a magnitude of 400 
V/m. What is the potential difference from the co-ordinate origin to the following points? 
(a) x = 0, y = 20 cm, z = 0 (b) x = 0, y = -30cm, z = 0 (c) x = 0, y = 0, z = 15cm 
Q 30.  An electric field of 20 N/C exists along the x-axis in space. Calculate the potential difference V
B
 - 
V
A 
where the points A and B are given by : 
  (a) A = (0, 0), B = (4m, 2m)  (b) A = (4m, 2m), B = (6m, 5m) 
Q 31.  The electric potential existing in space is V(x, y, z)= A (xy + yz + zx). 
(a) Write the dimensional formula of A. (b) Find the expression for the electric field. 
  (c) If A is 10 SI units, find the magnitude of the electric field at (1m, 1m, 1m) 
Q 32.  An electric field 
ˆˆ
E (20i 30j)N/ C ??
?
 
exists in the space. If the potential at the origin is taken to be 
zero, find the potential at (2 m, 2 m) 
Q 33.  In a certain region of space, the electric potential is V (x, y, z) = Axy - Bx
2
 + Cy, where A, B and 
C are positive constants. 
(a) Calculate the x, y and z components of the electric field. 
(b) At which points is the electric field equal to zero?  
  Gauss Theorem 
Q 34.  A sphere centered at the origin has radius 0.200 m. A - 500 ?C point charge is on the x-axis at x = 
0.300 m. The net flux through the sphere is 360 N m
2
/C What is the total charge inside the sphere? 
Q 35.  (a) A closed surface encloses a net charge of -3.60 ?C What is the net electric flux through the 
surface? 
(b) The electric flux through a closed surface is found to be 780 N-m
2
 /C What quantity of charge 
is enclosed by the surface? 
(c) The closed surface in part (b) is a cube with sides of length 2.50 cm. From the information 
given in part (b), is it possible to tell where within the cube the charge is located? Explain. 
Q 36.  The electric field in a region is given by 
0
34
ˆˆ
E E0i E j
55
??
?
 
with E
0
 =2.0 × 10
3
 N/C. Find the flux 
 of this field through a rectangular surface of area 0.2 m
2
 parallel to the Y-Z plane. 
Q 37.  The electric field in a region is given by 
0
Ex
ˆ
Ei
l
?
?
.
 
Find the charge contained inside a cubical 
volume bounded by the surfaces x= 0,x = a, y= 0, y = a, z = 0 and z = a. Take E
0
 = 5 × 10
3
 N/C, l 
= 2cm and a = 1 cm. 
Page 5


Exercises 
For JEE Main 
Subjective Questions 
  Note : You can take approximations in the answers. 
  Coulomb's Law 
Q 1.  A certain charge Q is divided into two parts q and Q - q, which are then separated by a certain 
distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two 
charges? 
Q 2.  Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible 
magnitude of the electric force acting on each charge? 
Q 3.  An ?-particle is the nucleus of a helium atom. It has a mass m = 6.64 × 10
-27
 kg and a charge q - + 
2e = 3.2 × 10
-19
 C. Compare the force of the electric repulsion between two ?-particles with the 
force of gravitational attraction between them. 
Q 4.  Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of 
0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the 
spheres. When the wire is removed, the spheres repel each other with an electrostatic force of 
0.0360 N. What were the initial charges on the spheres? 
Q 5.  Point charges q
1
 and q
2
 lie on the x-axis at points x = - a and x = + a respectively. 
(a) How must q
1
 and q
2
 be related for the net electrostatic force on point charge + Q, placed at x = 
+ a/2, to be zero? 
  (b) With the same point charge +Q now placed at x = + 3a/2. 
Q 6.  Two particles (free to move) with charges +q and +4q are a distance L apart. A third charge is 
placed so that the entire system is in equilibrium. 
  (a) Find the location, magnitude and sign of the third charge. 
  (b) Show that the equilibrium is unstable. 
Q 7.  Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of 
radius R with frictionless, non-conducting walls, the beads move, and at equilibrium they are a 
distance R apart (figure). Determine the charge on each bead.  
 
Q 8.  Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a 
length of l = 20cm. What charges should be imparted to the balls for each thread to form an angle 
of ? = 30?
 
with the vertical? 
  Electric Field 
Q 9.  Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The 
distance of each corner from the centre is a. Find the electric field at the centre of the pentagon. 
Q 10.  Three charges, each equal to q, are placed at the three corners of a square of side a. Find the 
electric field at fourth corner. 
Q 11.  A point charge q = -8.0 nC is located at the origin. Find the electric field vector at the point x = 1.2 
m, y = - 1.6 m. 
Q 12.  Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear 
charge density is ?. 
Q 13.  Find the electric field at a point P on the perpendicular bisector of a unifromly charged rod. The 
length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a. 
Q 14.  Find the direction of electric field at point P for the charge distribution as shown in figure. 
  (a)    (b)    (c)  
Q 15.  A clock face has charges - q, - 2q, - 3q,.. . - 12q fixed at the position of the corresponding 
numerals on the dial. The clock hands do not disturb the net field due to point charges. At what 
time does the hour hand point in the direction of the electric field at the centre of the dial. 
  Electric Forces 
Q 16.  An electron with a speed of 5.00 × 10
8
 cm/s enters an electric field of magnitude 1.00 × 10
3
 N/C, 
travelling along the field lines in the direction that retards its motion. 
(a) How far will the electron travel in the field before stopping momentarily and 
(b) How much time will have elapsed? 
(c) If the region with the electric field is only 8.00 mm long (too short from the electron to stop 
with in it), what fraction of the electron's initial kinetic energy will be lost in that region? 
Q 17.  A charged particle of mass m = 1 kg and charge q = 2 ?C is thrown from a horizontal ground at an 
angle ? = 45? with the speed 25 m/s. In space a horizontal electric field E = 2 × 10
7
 V/m exist in 
the direction of motion. Find the range on horizontal ground of the projectile thrown. Take g = 10 
m/s
2
. 
Q 18.  Protons are projected with an initial speed v
i
 = 9.55 × 10
3
 m/s into a region where a uniform 
electric field
ˆ
E ( 720j)N/ C ??
?
 
is present, as shown in figure. The protons are to hit a target that 
lies at a horizontal distance of 1.27 mm from the point where the protons are launched. Find : 
(a) the two projection angles ?
 
that result in a hit and 
(b) the total time of flight for each trajectory.  
 
Q 19.  At some instant the velocity components of an electron moving between two charged parallel 
plates are v
x
 = 1.5 × 10
5
 m/s and v
y
 = 3.0 × 10
6
 m/s. Suppose that the electric field between the 
plates is given by 
   
ˆ
E (120N/ C)j ?
?
 
(a) What is the acceleration of the electron? 
(b) What will be the velocity of the electron after its x-coordinate has changed by 2.0 cm? 
Electric Potential and Electric Potential Energy 
Q 20.  A point charge q
1
 = +2 ?C is placed at the origin of co-ordinates. A second charge, q
2
 = - 3 ?C, is 
placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute 
potential be zero?  
 
Q 21.  A charge Q is spread uniformly in the form of a line charge density 
Q
3a
?? on the sides of an 
equilateral triangle of perimeter 3a. Calculate the potential at the centriod C of the triangle. 
Q 22.  A uniform electric field of magnitude 250 V/m is directed in the positive x-direction. A + 12 ?C 
charge moves from the origin to the point (x, y) = (20.0cm, 5.0cm). 
(a) What was the change in the potential energy of this charge? 
(b) Through what potential difference did the charge move? 
Q 23.  A small particle has charge -5.00 ?C and mass 2.00 × 10
-4
 Kg. it moves from points, where the 
electric potential is V
A
 =+ 200 V, to point B, where the electric potential is V
B
 = + 800 V. The 
electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. 
What is its speed at point B ? Is it moving faster or slower at B than at A ? Explain. 
Q 24.  A plastic rod has been formed into a circle of radius R. It has a positive charge +Q uniformly 
distributed along one-quarter of its circumference and a negative charge of - 6Q uniformly 
distributed along the rest of the circumference (figure). With V = 0 at infinity, what is the electric 
potential 
(a) at the centre C of the circle and 
(b) at point P, which is on the central axis of the circle at distance z from the centre? 
 
Q 25.  A point charge q
1
 = + 2.40 ?C is held stationary at the origin. A second point charge q
2
 = -4.30 ?C 
moves from the point x = 0.150m, y = 0 to the point x = 0.250 m, y = 0.250 m. How much work is 
done by the electric force on q
2
? 
Q 26.  A point charge q
1
 = 4.00 nC is placed at the origin, and a second point charge q
2
= - 3.00 nC is 
placed on the x-axis at x = + 20.0cm A third point charge q
3
 = 2.00 nC is placed on the x-axis 
between q
1
 and q
2
. (Take as zero the potential energy of the three charges when they are infinitely 
far apart). 
(a) What is the potential energy of the system of the three charges if q
3
 is placed at x= +10.0cm ? 
(b) Where should q
3
 be placed to make the potential energy of the system equal to zero? 
Q 27.  Three point charges, which initially are infinitely far apart, are placed at the corners of an 
equilateral triangle with sides d. Two of the point charges are identical and have charge q. If zero 
net work is required to place the three charges at the corners of the triangles, what must the value 
of the third charge be? 
  Relation between Electric Field and Potential 
Q 28.  The electric field in a certain region is given by 
ˆˆ
E 5i 3jkV/ m ??
?
.
 
Find the difference in potential 
V
B
 - V
A
 . If A is at the origin and point B is at 
(a) (0, 0, 5) m,   (b) (4,0,3)m. 
Q 29.  In a certain region of space, the electric field is along +y direction and has a magnitude of 400 
V/m. What is the potential difference from the co-ordinate origin to the following points? 
(a) x = 0, y = 20 cm, z = 0 (b) x = 0, y = -30cm, z = 0 (c) x = 0, y = 0, z = 15cm 
Q 30.  An electric field of 20 N/C exists along the x-axis in space. Calculate the potential difference V
B
 - 
V
A 
where the points A and B are given by : 
  (a) A = (0, 0), B = (4m, 2m)  (b) A = (4m, 2m), B = (6m, 5m) 
Q 31.  The electric potential existing in space is V(x, y, z)= A (xy + yz + zx). 
(a) Write the dimensional formula of A. (b) Find the expression for the electric field. 
  (c) If A is 10 SI units, find the magnitude of the electric field at (1m, 1m, 1m) 
Q 32.  An electric field 
ˆˆ
E (20i 30j)N/ C ??
?
 
exists in the space. If the potential at the origin is taken to be 
zero, find the potential at (2 m, 2 m) 
Q 33.  In a certain region of space, the electric potential is V (x, y, z) = Axy - Bx
2
 + Cy, where A, B and 
C are positive constants. 
(a) Calculate the x, y and z components of the electric field. 
(b) At which points is the electric field equal to zero?  
  Gauss Theorem 
Q 34.  A sphere centered at the origin has radius 0.200 m. A - 500 ?C point charge is on the x-axis at x = 
0.300 m. The net flux through the sphere is 360 N m
2
/C What is the total charge inside the sphere? 
Q 35.  (a) A closed surface encloses a net charge of -3.60 ?C What is the net electric flux through the 
surface? 
(b) The electric flux through a closed surface is found to be 780 N-m
2
 /C What quantity of charge 
is enclosed by the surface? 
(c) The closed surface in part (b) is a cube with sides of length 2.50 cm. From the information 
given in part (b), is it possible to tell where within the cube the charge is located? Explain. 
Q 36.  The electric field in a region is given by 
0
34
ˆˆ
E E0i E j
55
??
?
 
with E
0
 =2.0 × 10
3
 N/C. Find the flux 
 of this field through a rectangular surface of area 0.2 m
2
 parallel to the Y-Z plane. 
Q 37.  The electric field in a region is given by 
0
Ex
ˆ
Ei
l
?
?
.
 
Find the charge contained inside a cubical 
volume bounded by the surfaces x= 0,x = a, y= 0, y = a, z = 0 and z = a. Take E
0
 = 5 × 10
3
 N/C, l 
= 2cm and a = 1 cm. 
Q 38.  A point charge Q is located on the axis of a disc of radius R at a distance b from the plane of the 
disc (figure). Show that if one-fourth of the electric flux from the charge passes through the disc, 
then R 3b ? .
 
 
Q 39.  A cube has sides of length L. It is placed with one corner at the origin as shown in figure. The 
electric field is uniform and given by 
ˆ ˆ ˆ
E Bj Cj Dk ? ? ? ?
?
, where B, C and D are positive constants. 
 
(a) Find the electric flux through each of the six cube faces S
1
,S
2
,S
3
,S
4
,S
5
 and S
6
. 
(b) Find the electric flux through the entire cube. 
Q 40.  Two point charges q and -q are separated by a distance 2l. Find the flux of electric field strength 
vector across the circle of radius R placed with its centre coinciding with the midpoint of line 
joining the two charges in the perpendicular plane. 
Q 41.  A point charge q is placed at the origin. Calculate the electric flux through the open hemispherical 
surface : (x - a)
2
 + y
2
 + z
2
 =a
2
 ,x ? a 
  Spherical Surfaces 
Q 42.  A charge Q is distributed over two concentric hollow spheres of radii r and R (> r) such that the 
surface charge densities are equal. Find the potential at the common centre. 
Q 43.  Three concentric metallic shells A, B and C of radii a, b and c(a<b< c) have surface charge 
densities, ?, - ? and ?
 
respectively. 
 
(a) Find the potentials of three shells A, B and C. 
(b) It is found that no work is required to bring a charge q from shell A to shell C then obtain the 
relation between the radii a, b and c. 
Q 44.  A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a, 
(a) Find the surface charge density on the inner surface and on the outer surface.