# Physics Questions and Answers – Potential Energy in an External Field

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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Potential Energy in an External Field”.

1. Pick out the expression of electric potential energy from the following.
a) U = $$\frac {1}{(4\pi \varepsilon_o)} \times [ \frac {q_1q_2}{r} ]$$
b) U = 1 × (4πεo) × [ $$\frac {q_1q_2}{r}$$ ]
c) U = $$\frac {1}{(4\pi \varepsilon_o)} \times [ \frac {q_1}{q_2}{r} ]$$
d) U = $$\frac {1}{(4\pi \varepsilon_o)}$$ × [q1q2]

Explanation: electric potential energy of a system of charges is the total amount of work done in bringing the various charges to their respective positions from infinitely large mutual separations.
The expression for electric potential energy is given by:
U = $$\frac {1}{(4\pi \varepsilon_o)} \times [ \frac {q_1q_2}{r} ]$$

2. Two isolated metallic spheres, one with a radius R and another with a radius 5R, each carries a charge ‘q’ uniformly distributed over the entire surface. Which sphere stores more electric potential energy?
a) The sphere with radius 5R
b) Both of the spheres will have the same energy
c) The sphere with radius R
d) Initially it will be the sphere with radius 5R then it will shift to the sphere with radius R

Explanation: The sphere with radius R stores more electric potential energy. According to the electric potential energy equation → U = $$\frac {1}{(4\pi \varepsilon_o)} \times [ \frac {q_1q_2}{r} ]$$ Potential energy is inversely proportional to radius. Therefore, the sphere with lesser radius will store more energy. So, the smaller sphere will store more energy.

3. There are two charges → Q1 = +q and charge Q2 = +2q. From the initial point (Q), Q1 is at a distance of r and Q2 is at a distance 2r. Which charge (Q1 or Q2) will have higher electrostatic potential energy?
a) Q1
b) Both will have the same energy
c) Q2
d) The information given is not enough to determine

Explanation: Electrostatic potential energy of Q1 → U1 = $$\frac {1}{(4\pi \varepsilon_o)}$$ × [Q × $$\frac {q}{r}$$] ……….1
Electrostatic potential energy of Q2 → U2 = $$\frac {1}{(4\pi \varepsilon_o)}$$ × [Q × $$\frac {2q}{2r}$$]
→ U2 = $$\frac {1}{(4\pi \varepsilon_o)}$$ × [Q x $$\frac {q}{r}$$] ………2
1 = 2
Therefore, both the charges will have the same energy.

4. Electrostatic potential energy can be negative.
a) True
b) False

Explanation: If the charge ‘q’ is negative, the sign should be considered in the equation. Therefore, a system consisting of negative and positive point charges will have negative potential energy. A negative potential energy means that work must be done against the electric field in order to move the charges apart.

5. Identify the dimension of electrostatic potential energy from the following.
a) ML2T-3A-2
b) ML3T-2A-1
c) M-1L2T-3A
d) ML2T-3A-1

Explanation: Electrostatic potential energy is a scalar quantity that means it possesses only magnitude and no direction. This quantity is denoted by U and it is measured in joules (J). The dimensional formula of electrostatic potential energy is ML2T-3A-1.