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Multiple Choice Questions (MCQs): Electrostatic Potential - JEE MCQ


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20 Questions MCQ Test - Multiple Choice Questions (MCQs): Electrostatic Potential

Multiple Choice Questions (MCQs): Electrostatic Potential for JEE 2025 is part of JEE preparation. The Multiple Choice Questions (MCQs): Electrostatic Potential questions and answers have been prepared according to the JEE exam syllabus.The Multiple Choice Questions (MCQs): Electrostatic Potential MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Multiple Choice Questions (MCQs): Electrostatic Potential below.
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Multiple Choice Questions (MCQs): Electrostatic Potential - Question 1

The minimum velocity v with which charge q should be projected so that it manages to reach the centre of the ring starting from the position shown in figure is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 1

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 2

According to the standard convention, the electric potential at a point infinitely far from a charge is taken to be:

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 2

The standard convention states that the electric potential at a point infinitely far from a charge is considered to be:

  • Zero

This means that as you move further away from a charge, the potential energy associated with that charge diminishes to zero.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 3

A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9 C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) is​

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 3

Solution:

To calculate the work done in moving a charge in an electric field, we use the formula:

  • Work = Charge × Voltage Difference

Here, we have:

  • Charge = -2 x 10-9 C
  • Initial position P = (0, 3 cm, 0)
  • Final position Q = (0, 4 cm, 0)

The voltage (potential) at a distance r from a point charge is given by:

  • V = k × Q / r
  • Where k = 9 x 109 Nm2/C2 and Q = 6 mC = 6 x 10-3 C

Calculating the voltage at points P and Q:

  • At P (0, 3 cm): r = 0.03 m
  • VP = (9 x 109) × (6 x 10-3) / 0.03 = 1.8 x 106 V
  • At Q (0, 4 cm): r = 0.04 m
  • VQ = (9 x 109) × (6 x 10-3) / 0.04 = 1.35 x 106 V

Now, the voltage difference:

  • ΔV = VQ - VP = 1.35 x 106 - 1.8 x 106 = -0.45 x 106 V

Finally, calculating the work done:

  • Work = (-2 x 10-9) × (-0.45 x 106) = 0.0009 J = 0.9 J

Thus, the work done is 0.9 J.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 4

On moving a charge of 20 coulombs by 2 cm, 2 J of work is done, then the potential difference between the points is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 4

Potential difference between two points is given by

Va - Vb = W/q0

Work, W = 2 J

Charge, q0 = 20 C

Potential difference = 2/20 = 0.1 V

The correct option is C.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 5

A charge is uniformly distributed inside a spherical body of radius r1 = 2r0 having a concentric cavity of radius r2 = r0 (ρ is charge density inside the sphere). The potential of a point P or  a distance 3r0/2 from the centre is

 

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 5

Electric field at a distance r,
(r0 < r < 2r0) from the center is given by

Potential at the outer surface,

∴ If V is the required potential at r  = 3r0/2,

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 6

Electric field intensity at point ‘B’ due to a point charge ‘Q’ kept at a point ‘A’ is 12 NC-1 and the electric potential at a point ‘B’ due to same charge is 6 JC-1. The distance between AB is​

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 6

E.l = V   where,
E = electric field intensity = 12 N/C
V = electric potential = 6 J/C
=> distance between A and B, 
l = (6 / 12) m or (1 / 2) m = 0.5 m
 

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 7

Work done in carrying 2C charge in a circular path of radius 2m around a charge of 10C is​

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 7

The overall work performed in carrying a 2coulomb charge in a circular orbit of radius 3 m around a charge of 10 coulomb is calculated below.
It is a well-known fact that W=qdv.
Here dV is the change in overall potential. In the circular orbit of r potential at each point is similar.
Most significantly, the value of r is 3.  
The value of dv=0 and hence W=q0=0.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 8

Dimensional formula for potential difference is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 8

The electric potential difference (V) is defined as the work done (W) per unit charge (q):

V = W / q

  • Work done (W) has the dimensional formula: [M L² T⁻²]

  • Charge (q) has the dimensional formula: [A T]

Now divide the two:

[V] = [M L² T⁻²] / [A T] = [M L² T⁻³ A⁻¹]

Hence, the dimensional formula of potential difference is: [M L² T⁻³ A⁻¹]

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 9

If 100 J of work has to be done in moving an electric charge of 4C from a place where potential is -5 V to another place, where potential is V volt. The value of V is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 9

From the definition, the work done to a test charge ‘q0’ from one place to another place in an electric field is given by the formula
W=q0x[vfinal-vinitial ]
100=4x[v-(-5)]
v+5=25
v=20V
 

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 10

A particle of charge q1 = 3μC is located on x-axis at the point x1 = 6 cm. A second point charge q2 = 2μC is placed on the x-axis at x2 = -4 cm. The absolute electric potential at the origin is​

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 10

The absolute electric potential at the origin due to two point charges can be calculated using the formula:

  • V = k (q1/r1 + q2/r2)

Where:

  • V = electric potential
  • k = 8.99 x 109 N m2/C2 (Coulomb's constant)
  • q1 = 3 µC (charge at x1 = 6 cm)
  • q2 = 2 µC (charge at x2 = -4 cm)
  • r1 = 6 cm = 0.06 m (distance from origin to q1)
  • r2 = 4 cm = 0.04 m (distance from origin to q2)

Substituting the values:

  • V = 8.99 x 109 × (3 x 10-6/0.06 + 2 x 10-6/0.04)

Calculating each term:

  • For q1: 3 x 10-6/0.06 = 5 x 10-5
  • For q2: 2 x 10-6/0.04 = 5 x 10-5

Therefore:

  • V = 8.99 x 109 × (5 x 10-5 + 5 x 10-5)
  • V = 8.99 x 109 × 10 x 10-5 = 8.99 x 105 V

Thus, the absolute electric potential at the origin is: 9 x 105 V.

 

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 11

Two spheres of radii r and R carry charges q and Q respectively. When they are connected by a wire, there will be no loss of energy of the system if

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 11

There will be no loss of energy if the potential of the spheres is the same i.e. if

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 12

Electric potential is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 12

Electric potential is the electric potential energy per unit charge. In equation form, V=U/q, where U is the potential energy, q is the charge, and V is the electric potential. Since both the potential energy and charge are scalar quantities, so does the potential.
And it's dimension [ L2M1T-3I-1]

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 13

In the figure shown, conducting shells A and B have charges Q and 2Q distributed uniformly over A and B.Value of VA − VB is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 13

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 14

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 14

Let λ be the charge density on the inner cylinder.

For a < r < b, we get

Hence, a potential difference appears between the two cylinders when a charge density is given to the inner cylinder.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 15

The electric potential at a point (x,y) is given by: V=−Kxy. The electric field intensity a distance r from the origin varies as

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 15

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 16

Equal charges are given to two spheres of different radii. The potential will

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 16

When equal charges are given to two spheres of different radii, the potential will be more or the smaller sphere as per the equation, Potential = Charge / Radius.
Since potential is inversely proportional to radius, the smaller radius will have higher potential and vice versa.

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 17

A charge −q is placed at the axis of a charged ring of radius r at a distance of 2√2r as shown in figure. If ring is fixed and carrying a charge Q, the kinetic energy of charge −q when it is released and reaches the centre of ring will be

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 17


Multiple Choice Questions (MCQs): Electrostatic Potential - Question 18

Consider a solid cube made up of insulating material having a uniform volume charge density. Assuming the electrostatic potential to be zero at infinity, the ratio of the potential at a corner of the cube to that at the centre will be 

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 18

By dimensional analysis

but by superposition

Because of the centre of the larger cube lies at a corner of the eight smaller cubes of which it is made
therefore,

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 19

Electric potential varies with distance such that V(x) =ax-bx3; where a and b are constants. Where will the electric field intensity be zero?

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 19

Multiple Choice Questions (MCQs): Electrostatic Potential - Question 20

Half part of ring is uniformly positively charged and other half is uniformly negatively charged. Ring is in equilibrium in uniform electric field as shown and free to rotate about an axis passing through its centre and perpendicular to plane. The equilibrium is

Detailed Solution for Multiple Choice Questions (MCQs): Electrostatic Potential - Question 20

Assuming ring as dipole, then dipole moment   and  are in same direction, so potential energy U =−PE

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