Electrostatic Potential Energy - Free MCQ Practice Test with solutions,

From conservation of angular momentum,

from conservation of energy,

To find the change in potential energy of an electron in a uniform electric field:

The formula for potential energy change (ΔU) in an electric field is:

• ΔU = q × V × h

Where:

• q = charge of the electron (approximately 1.6 × 10^-19 C)
• V = electric field strength (100 V/m)
• h = height change (0.5 m)

Calculating the change in potential energy:

• ΔU = (1.6 × 10^-19 C) × (100 V/m) × (0.5 m)
• ΔU = 8 × 10^-18 J

To convert joules to electron volts (eV):

• 1 eV = 1.6 × 10^-19 J
• ΔU in eV = (8 × 10^-18 J) / (1.6 × 10^-19 J/eV) = 50 eV

Thus, the change in potential energy of the electron is 50 eV.

Definition based

Since Potential difference between two points in equipotential surfaces is zero, the work done between two points in equipotential surface is also zero.

Definition based

Correct option: B - Infinity.

The mutual interaction energy between distinct charges is absent, so the mutual contribution would be zero, but this does not include the self-energy of a point charge.

U = (ε₀/2) ∫ E² dV is the expression for electrostatic energy stored in the field.

E = q/(4π ε₀ r²) for a point charge.

Therefore E² ∝ 1/r⁴ and with the volume element dV = 4π r² dr the integrand behaves like 1/r²; the radial integral near the origin is like ∫ (1/r²) dr, which diverges as r → 0.

Hence the self-energy of a classical point charge is infinite, and the total electrostatic energy including self-energy is infinite. Thus option B is correct.

If one intentionally excludes self-energy and counts only interaction energy between distinct charges, the energy would be zero; the difference between these interpretations explains the ambiguity unless the question specifies inclusion or exclusion of self-energy.

K = qV

We know that energy required/gained = force x displacement
As F = kqQ / r² and displacement is r
We get U = kQq /r
Where k = 1/4ϵ

The electrostatic potential energy U of a system containing two point charges can be calculated using the formula:

Where:

• k is Coulomb's constant, k = 8.99 × 10⁹N⋅m²/C²
• q₁​ and q₂ are the magnitudes of the charges,
• r is the distance between the charges.

Given:

• q₁ = 40 nC = 40 × 10⁻⁹ C,
• q₂ = 60 nC = 60 × 10⁻⁹ C,
• r = 36 cm = 0.36m.

Substituting the values into the formula:

So, Optiob (B) is the correct answer.

Given,

The distance between them  when the electrostatic energy between two charges q₁ and q₂ is given as 

According to the principle of superposition, total energy of the charge system as shown in the figure below is