Electrostatic potential energy — NEET & JEE Questions

Question 1 · difficulty L1 · recall

What is the electrostatic potential energy of two point charges $q_1$ and $q_2$ separated by a distance $r$ in vacuum, taking zero potential energy at infinite separation?

• A. $\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r}$
• B. $\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}$
• C. $\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1+q_2}{r}$
• D. $\dfrac{1}{4\pi\varepsilon_0}q_1q_2r$

Question 2 · difficulty L2 · understanding

Two positive point charges are brought from infinite separation to a finite distance apart. What is the sign of their electrostatic potential energy?

• A. Positive
• B. Negative
• C. Zero
• D. It must alternate with distance

Question 3 · difficulty L2 · understanding

A positive and a negative point charge are brought closer together from rest. How does their electrostatic potential energy change?

• A. It increases toward positive values
• B. It decreases and becomes more negative
• C. It remains zero
• D. It is independent of separation

Question 4 · difficulty L2 · understanding

If a charge $q$ is moved between two points whose electric potentials are $V_A$ and $V_B$, what is the change in its electrostatic potential energy?

• A. $q(V_B-V_A)$
• B. $q(V_A-V_B)$
• C. $(V_B-V_A)/q$
• D. $q(V_A+V_B)$

Question 5 · difficulty L3 · application

Two point charges $+2\,\mu\text{C}$ and $+3\,\mu\text{C}$ are $0.30\,\text{m}$ apart in vacuum. What is their electrostatic potential energy? Take $k=9\times10^9\,\text{N m}^2\text{C}^{-2}$.

• A. $0.018\,\text{J}$
• B. $0.18\,\text{J}$
• C. $1.8\,\text{J}$
• D. $18\,\text{J}$

Question 6 · difficulty L3 · application

A charge of $+5\,\mu\text{C}$ moves from a point at $20\,\text{V}$ to a point at $80\,\text{V}$. What is the change in its electrostatic potential energy?

• A. $-3.0\times10^{-4}\,\text{J}$
• B. $+3.0\times10^{-4}\,\text{J}$
• C. $+5.0\times10^{-4}\,\text{J}$
• D. $+6.0\times10^{-5}\,\text{J}$

Question 7 · difficulty L3 · application

Three charges $+q$, $+q$ and $-q$ are placed at the vertices of an equilateral triangle of side $a$. What is the total electrostatic potential energy of the system?

• A. $+\dfrac{kq^2}{a}$
• B. $-\dfrac{kq^2}{a}$
• C. $-\dfrac{2kq^2}{a}$
• D. $0$

Question 8 · difficulty L3 · application

A charge $-2\,\mu\text{C}$ moves from $50\,\text{V}$ to $10\,\text{V}$. What is the change in its electrostatic potential energy?

• A. $-80\,\mu\text{J}$
• B. $+80\,\mu\text{J}$
• C. $-120\,\mu\text{J}$
• D. $+120\,\mu\text{J}$

Question 9 · difficulty L4 · application

Charges $+2\,\mu\text{C}$, $+2\,\mu\text{C}$ and $-1\,\mu\text{C}$ are placed at the vertices of an equilateral triangle of side $0.20\,\text{m}$. What is the total electrostatic potential energy? Take $k=9\times10^9\,\text{N m}^2\text{C}^{-2}$.

• A. $-0.18\,\text{J}$
• B. $0$
• C. $+0.09\,\text{J}$
• D. $+0.18\,\text{J}$

Question 10 · difficulty L4 · application

Two fixed charges $+4\,\mu\text{C}$ and $+1\,\mu\text{C}$ are $3.0\,\text{m}$ apart. A charge $-2\,\mu\text{C}$ is brought from infinity to a point between them, $1.0\,\text{m}$ from the $+4\,\mu\text{C}$ charge. What external work is required for a slow placement? Take $k=9\times10^9$ in SI units.

• A. $-81\,\text{mJ}$
• B. $-90\,\text{mJ}$
• C. $+81\,\text{mJ}$
• D. $+90\,\text{mJ}$