J J Science Academy

Q1. Three charges, $+q$, $+q$, $-q$, are placed at the three corners of an equilateral triangle, of side $L$. The potential energy of the system is

1) $V=0, E = 0$

2) $V=0, E \neq 0$

3) $V \neq 0, E=0$

4) $V \neq 0, E \neq 0$

Q2. Two similar charged small spheres, each having a charge $Q$ are suspended from a point by a thread of length $L$ . At equilibrium, the angle made by the threads with the vertical is $30^{\circ}$. The electrostatic PE of the system at equilibrium, is

1) $\frac{kQ^2}{L}$

2) $\frac{\sqrt{3} kQ^2}{2 L}$

3) $\frac{kQ^2}{\sqrt{3} L}$

4) $\frac{\sqrt{3} kQ^2}{L}$

Q3. P.E. of system of charges, shown in the figure, is

1) $\frac{3}{4 \pi \varepsilon_0} \frac{q^2}{r}$

2) $\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{r}$

3) $-\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{r}$

4) $-\frac{3}{4 \pi \varepsilon_0} \frac{q^2}{r}$

Q4. The value of $Q$ , for which the PE of system is zero, is

1) $-\frac{q}{\sqrt{2}}$

2) $-0.47 q$

3) $-\sqrt{2} q$

4) $\frac{q}{\sqrt{2}}$

Q5. Three positive charges are placed at the vertices of an equilateral triangle. A negative charge is placed at the centre of the triangle. The P.E of the system will

1) Increase

Q6. Three charges $1 \times 10^{-8} C$, $2 \times 10^{-8} C$ and $3 \times 10^{-8} C$ are placed at $x=1 cm$, $x=2 cm$, and $x=3 cm$, respectively, on x -axis from the origin. The potential energy of this arrangement relative to the potential energy for infinite separation is

1) $7.9 \times 10^{-2} J$

2) $8.55 \times 10^{-4} J$

3) $6.5 \times 10^{-7} J$

4)

Hint: $U = U_1 + U_2 + U_3$ $=$ $\frac{1}{4\pi\varepsilon_0}(\frac{q_1 q_2}{r_{12}}+\frac{q_2 q_3}{r_{23}}+\frac{q_1 q_3}{r_{13}})$ $=$ $9 \times 10^9 \times [ \frac{2 \times 10^{-16}}{1 \times 10^{-2}} + \frac{6 \times 10^{-16}}{1 \times 10^{-2}} + \frac{3 \times 10^{-16}}{2 \times 10^{-2}} ]$ $=$ $9 \times 10^9 \times [ (2 + 6 + 1.5) \times 10^{-14} ]$ $=$ $9 \times 10^9 \times 9.5 \times 10^{-14} = 8.55 \times 10^{-4} J$