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# ELECTRIC FLUX AND GAUSS LAW Electrical Engineering (EE) Notes | EduRev

## Electrical Engineering (EE) : ELECTRIC FLUX AND GAUSS LAW Electrical Engineering (EE) Notes | EduRev

``` Page 1

1
ELECTRIC FLUX AND GAUSS LAW
2EL-01
1. The three small spheres as shown in figure,
carry charges q
1
= 4.0 nC, q
2
= -8.0 nC and
q
3
= 2.0 nC. Find the net electric flux
through each of the following closed
surfaces shown in cross section in the figure.

2. A charge Q is
distributed uniformly
on a ring of radius r. A
is constructed with its centre at the periphery
of the ring. Find the flux of the electric field
through the surface of the sphere.
3. Figure shows an imaginary cube of edge L/2.
A uniformly charged rod of length L moves
towards left at a small but constant speed v.
At t = 0, the left end just touches the centre
of the face of the cube opposite it. Which of
the graphs shown in figure represents the
flux of the electric field through the cube as
the rod goes through it?
L/2
L
v
(a)
Flux
a
b
c
d
time (b)

4. A hemispherical body is placed in a uniform
electric field E. What is the flux linked with
the curved surface, if field is (a) parallel to
base figure (a), (b) perpendicular to base
figure (b).

R
n
(A)
E

R
n
(B)
E

(C )
E
n
R

5. What is the field in the cavity, if a conductor
having a cavity is charged ? Does the result
depend on the shape and size of cavity or
conductor?
6. Figure shows a closed surface which
intersects a conducting sphere. If a positive
charge is placed at the points P.  Find the
sign of flux passing through curved surface
‘s’.

7. In which position (A, B, C or D) of second
charge the flux of the electric field through
the hemisphere remains uncharged.
A
B
C
D
q

Ring
A
B
0
1
Sphere
0
Page 2

1
ELECTRIC FLUX AND GAUSS LAW
2EL-01
1. The three small spheres as shown in figure,
carry charges q
1
= 4.0 nC, q
2
= -8.0 nC and
q
3
= 2.0 nC. Find the net electric flux
through each of the following closed
surfaces shown in cross section in the figure.

2. A charge Q is
distributed uniformly
on a ring of radius r. A
is constructed with its centre at the periphery
of the ring. Find the flux of the electric field
through the surface of the sphere.
3. Figure shows an imaginary cube of edge L/2.
A uniformly charged rod of length L moves
towards left at a small but constant speed v.
At t = 0, the left end just touches the centre
of the face of the cube opposite it. Which of
the graphs shown in figure represents the
flux of the electric field through the cube as
the rod goes through it?
L/2
L
v
(a)
Flux
a
b
c
d
time (b)

4. A hemispherical body is placed in a uniform
electric field E. What is the flux linked with
the curved surface, if field is (a) parallel to
base figure (a), (b) perpendicular to base
figure (b).

R
n
(A)
E

R
n
(B)
E

(C )
E
n
R

5. What is the field in the cavity, if a conductor
having a cavity is charged ? Does the result
depend on the shape and size of cavity or
conductor?
6. Figure shows a closed surface which
intersects a conducting sphere. If a positive
charge is placed at the points P.  Find the
sign of flux passing through curved surface
‘s’.

7. In which position (A, B, C or D) of second
charge the flux of the electric field through
the hemisphere remains uncharged.
A
B
C
D
q

Ring
A
B
0
1
Sphere
0

2
ELECTRIC FLUX AND GAUSS LAW
2EL-01
8. A charge q is placed at the center of an
imaginary hemispherical surface. The flux of
the electric field due to the charge through
the surface of the hemisphere.
q

9. Find the flux of the electric field through
each of the five surfaces of the inclined plane
as shown in figure. What is the total flux
through the entire closed surface?

10. Consider two concentric conducting spheres.
The outer sphere is hollow and initially has a
charge -7Q on it. The inner sphere is solid
and has a charge +2Q on it.
(a) How much charge is on the outer surface
and inner surface of the outer sphere.
(b) If a wire is connected between the inner
and outer spheres, after electrostatic
equilibrium is established, how much total
charge is on the outer sphere? How much
charge is on the outer surface and inner
surface of outer sphere? Does the electric
field at the surface of the inside sphere
change when the wire is connected?
now connect the outer sphere to ground will
be on the outer sphere? How much charge
will be on the inner surface and outer surface
of the outer sphere?
11. A cube of side l has one corner at the origin
of coordinates and extends along the positive
x, y and z-axes. Suppose the electric field in
this region is given by
ˆ
() E a by j ?? .
Determine the charge inside the cube.

12. The electric field in a cubical volume is

00
ˆˆ
1
zz
E E i E j
aa
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?

Each edge of the cube measures d and one of
the corners lies at the origin of coordinates.
Determine the net charge within the cube

13. A point charge is placed at a distance a/2
from the centre of a square of side ‘a’ as
shown in the diagram; calculate the electric
flux passing through the square.

Page 3

1
ELECTRIC FLUX AND GAUSS LAW
2EL-01
1. The three small spheres as shown in figure,
carry charges q
1
= 4.0 nC, q
2
= -8.0 nC and
q
3
= 2.0 nC. Find the net electric flux
through each of the following closed
surfaces shown in cross section in the figure.

2. A charge Q is
distributed uniformly
on a ring of radius r. A
is constructed with its centre at the periphery
of the ring. Find the flux of the electric field
through the surface of the sphere.
3. Figure shows an imaginary cube of edge L/2.
A uniformly charged rod of length L moves
towards left at a small but constant speed v.
At t = 0, the left end just touches the centre
of the face of the cube opposite it. Which of
the graphs shown in figure represents the
flux of the electric field through the cube as
the rod goes through it?
L/2
L
v
(a)
Flux
a
b
c
d
time (b)

4. A hemispherical body is placed in a uniform
electric field E. What is the flux linked with
the curved surface, if field is (a) parallel to
base figure (a), (b) perpendicular to base
figure (b).

R
n
(A)
E

R
n
(B)
E

(C )
E
n
R

5. What is the field in the cavity, if a conductor
having a cavity is charged ? Does the result
depend on the shape and size of cavity or
conductor?
6. Figure shows a closed surface which
intersects a conducting sphere. If a positive
charge is placed at the points P.  Find the
sign of flux passing through curved surface
‘s’.

7. In which position (A, B, C or D) of second
charge the flux of the electric field through
the hemisphere remains uncharged.
A
B
C
D
q

Ring
A
B
0
1
Sphere
0

2
ELECTRIC FLUX AND GAUSS LAW
2EL-01
8. A charge q is placed at the center of an
imaginary hemispherical surface. The flux of
the electric field due to the charge through
the surface of the hemisphere.
q

9. Find the flux of the electric field through
each of the five surfaces of the inclined plane
as shown in figure. What is the total flux
through the entire closed surface?

10. Consider two concentric conducting spheres.
The outer sphere is hollow and initially has a
charge -7Q on it. The inner sphere is solid
and has a charge +2Q on it.
(a) How much charge is on the outer surface
and inner surface of the outer sphere.
(b) If a wire is connected between the inner
and outer spheres, after electrostatic
equilibrium is established, how much total
charge is on the outer sphere? How much
charge is on the outer surface and inner
surface of outer sphere? Does the electric
field at the surface of the inside sphere
change when the wire is connected?
now connect the outer sphere to ground will
be on the outer sphere? How much charge
will be on the inner surface and outer surface
of the outer sphere?
11. A cube of side l has one corner at the origin
of coordinates and extends along the positive
x, y and z-axes. Suppose the electric field in
this region is given by
ˆ
() E a by j ?? .
Determine the charge inside the cube.

12. The electric field in a cubical volume is

00
ˆˆ
1
zz
E E i E j
aa
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?

Each edge of the cube measures d and one of
the corners lies at the origin of coordinates.
Determine the net charge within the cube

13. A point charge is placed at a distance a/2
from the centre of a square of side ‘a’ as
shown in the diagram; calculate the electric
flux passing through the square.

3
ELECTRIC FLUX AND GAUSS LAW
2EL-01
14. In figure shown a charge q is placed at a
distance ? =0 near one of the edges of a cube
of edge l on a line of symmetry along
diagonal.

(a) What is flux through each of the sides
containing the point a.
(b) What is the flux through the other three
faces?
15. Find the electric flux through cylindrical
surface in a uniform electric field E

16. What is the flux if the cylinder of previous
problem were vertical ?
17. Two identical metal plates each having
surface area ‘A’, having charge ‘q
1
’ and ‘q
2
’
are placed facing each other at a separation
‘d’. Find the charge appearing on surface (1),
(2), (3) and (4). Assume the size of the plate
is much longer than the separation between
the plates.

18. A point charge q is placed on the apex of a
cone of semi-vertex angle ?. Find the electric
flux through the base of the cone.

19. The cube as shown in figure has sides of
length L = 10.0 cm. The electric field is
uniform, has a magnitude E = 4.00 × 10
3

N/C, and is parallel to the xy-plane at an
angle of 37° measured from the +x axis
toward the +y-axis.

What is the electric flux through each of the
six cube faces S
1
, S
2
, S
3
, S
4
, S
5
and S
6
?
(b) What is the total electric flux through all
faces of the cube?
20. A cube has sides of length L = 0.300 m. It is
placed with one corner at the origin as shown
in the above figure. The electric field is not
uniform, but is given by
?
ˆ .
5.00 / . ) (3.00 N/C ) . E N C m xi m zk ? ? ?
Find the electric flux through each of the six
cube faces S
1
, S
2
, S
3
, S
4
, S
5
and S
6
and find
the total electric charge inside the cube.
Page 4

1
ELECTRIC FLUX AND GAUSS LAW
2EL-01
1. The three small spheres as shown in figure,
carry charges q
1
= 4.0 nC, q
2
= -8.0 nC and
q
3
= 2.0 nC. Find the net electric flux
through each of the following closed
surfaces shown in cross section in the figure.

2. A charge Q is
distributed uniformly
on a ring of radius r. A
is constructed with its centre at the periphery
of the ring. Find the flux of the electric field
through the surface of the sphere.
3. Figure shows an imaginary cube of edge L/2.
A uniformly charged rod of length L moves
towards left at a small but constant speed v.
At t = 0, the left end just touches the centre
of the face of the cube opposite it. Which of
the graphs shown in figure represents the
flux of the electric field through the cube as
the rod goes through it?
L/2
L
v
(a)
Flux
a
b
c
d
time (b)

4. A hemispherical body is placed in a uniform
electric field E. What is the flux linked with
the curved surface, if field is (a) parallel to
base figure (a), (b) perpendicular to base
figure (b).

R
n
(A)
E

R
n
(B)
E

(C )
E
n
R

5. What is the field in the cavity, if a conductor
having a cavity is charged ? Does the result
depend on the shape and size of cavity or
conductor?
6. Figure shows a closed surface which
intersects a conducting sphere. If a positive
charge is placed at the points P.  Find the
sign of flux passing through curved surface
‘s’.

7. In which position (A, B, C or D) of second
charge the flux of the electric field through
the hemisphere remains uncharged.
A
B
C
D
q

Ring
A
B
0
1
Sphere
0

2
ELECTRIC FLUX AND GAUSS LAW
2EL-01
8. A charge q is placed at the center of an
imaginary hemispherical surface. The flux of
the electric field due to the charge through
the surface of the hemisphere.
q

9. Find the flux of the electric field through
each of the five surfaces of the inclined plane
as shown in figure. What is the total flux
through the entire closed surface?

10. Consider two concentric conducting spheres.
The outer sphere is hollow and initially has a
charge -7Q on it. The inner sphere is solid
and has a charge +2Q on it.
(a) How much charge is on the outer surface
and inner surface of the outer sphere.
(b) If a wire is connected between the inner
and outer spheres, after electrostatic
equilibrium is established, how much total
charge is on the outer sphere? How much
charge is on the outer surface and inner
surface of outer sphere? Does the electric
field at the surface of the inside sphere
change when the wire is connected?
now connect the outer sphere to ground will
be on the outer sphere? How much charge
will be on the inner surface and outer surface
of the outer sphere?
11. A cube of side l has one corner at the origin
of coordinates and extends along the positive
x, y and z-axes. Suppose the electric field in
this region is given by
ˆ
() E a by j ?? .
Determine the charge inside the cube.

12. The electric field in a cubical volume is

00
ˆˆ
1
zz
E E i E j
aa
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?

Each edge of the cube measures d and one of
the corners lies at the origin of coordinates.
Determine the net charge within the cube

13. A point charge is placed at a distance a/2
from the centre of a square of side ‘a’ as
shown in the diagram; calculate the electric
flux passing through the square.

3
ELECTRIC FLUX AND GAUSS LAW
2EL-01
14. In figure shown a charge q is placed at a
distance ? =0 near one of the edges of a cube
of edge l on a line of symmetry along
diagonal.

(a) What is flux through each of the sides
containing the point a.
(b) What is the flux through the other three
faces?
15. Find the electric flux through cylindrical
surface in a uniform electric field E

16. What is the flux if the cylinder of previous
problem were vertical ?
17. Two identical metal plates each having
surface area ‘A’, having charge ‘q
1
’ and ‘q
2
’
are placed facing each other at a separation
‘d’. Find the charge appearing on surface (1),
(2), (3) and (4). Assume the size of the plate
is much longer than the separation between
the plates.

18. A point charge q is placed on the apex of a
cone of semi-vertex angle ?. Find the electric
flux through the base of the cone.

19. The cube as shown in figure has sides of
length L = 10.0 cm. The electric field is
uniform, has a magnitude E = 4.00 × 10
3

N/C, and is parallel to the xy-plane at an
angle of 37° measured from the +x axis
toward the +y-axis.

What is the electric flux through each of the
six cube faces S
1
, S
2
, S
3
, S
4
, S
5
and S
6
?
(b) What is the total electric flux through all
faces of the cube?
20. A cube has sides of length L = 0.300 m. It is
placed with one corner at the origin as shown
in the above figure. The electric field is not
uniform, but is given by
?
ˆ .
5.00 / . ) (3.00 N/C ) . E N C m xi m zk ? ? ?
Find the electric flux through each of the six
cube faces S
1
, S
2
, S
3
, S
4
, S
5
and S
6
and find
the total electric charge inside the cube.

4
ELECTRIC FLUX AND GAUSS LAW
2EL-01
21. A cube of side a is placed such that the
nearest face which is parallel to the y-z plane
is at a distance ‘a’ from the origin. The
electric field component are E
x
= ax
1/2
,
E
y
= E
z
= 0. Calculate

y
z
x

(a) the flux f
E
through the cube
(b) the charge within the cube
22. A very long uniformly charged wire oriented
along the axis of a circle of radius R rests on
its center with one of the ends (as shown in
figure). The linear charge density on the wire
is l. Evaluate the flux of vector E across the
circle area.
+ ?
R

23. Find the electric flux crossing the wire frame
ABCD of length l width b and whose center
is at a distance OP = d from an infinite line
of charge with linear charge density ?.
Consider that the plane of frame is
perpendicular to the line OP.
A
B
C
D
O
b
d
?
P

24. Two point charges q and -q separated by the
distance 2a. Evaluate the flux of electric
field strength vector across a circle of radius
R.
a a
-q +q
R

25. A solid spherical region having a spherical
cavity whose diameter ‘R’ is equal to the
radius of the spherical region, has a total
charge ‘Q’. Find the electric field at a point
P as shown.
P
R
x

26. An insulating sphere of radius R has a
spherical hole of radius a located within its
volume and centered a distance b from the
center of the sphere, where a < b < R  (a
cross section of the sphere is shown in
figure). The solid part of the sphere has a
uniform volume charge density ?. Find the
magnitude and direction of the electric
field E inside the hole, and show that E is
uniform over the entire hole.

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