What is the potential energy of two equal positive point charges of 1 μC each held 1 m apart in air?

1. $9\times {10}^{-\mathrm{3 }}J$

2. $9\times {10}^{-\mathrm{3 }}eV$

3. $\mathrm{2 }eV/m$

4. zero

Three charges Q, (+q) and (+q) are placed at the vertices of an equilateral triangle of side l as shown in the figure. If the net electrostatic energy of the system is zero, then Q is equal to:

1. $\left(-\frac{{\displaystyle q}}{{\displaystyle 2}}\right)$

2. (–q)

3. (+q)

4. Zero

A charge $q_1 = 5 \times {10}^{–8}$ C is kept at 3 cm from a charge $q_2 = –2 \times {10}^{–8} C$. The potential energy of the system relative to the potential energy at infinite separation is:

1. 3 x ${10}^{-4}$ J

2. –3 x ${10}^{-4}$ J

3. 9 x ${10}^{-6}$ J

4. –9 x ${10}^{-6}$ J

In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å. The potential energy of the system in eV is:
(Taking the zero of the potential energy at an infinite separation of the electron from the proton.)
1. -23.1 eV
2. 27.0 eV
3. -27.2 eV
4. 23.7 eV

An elementary particle of mass m and charge +e is projected with velocity v at a much more massive particle of charge Ze, where Z > 0. What is the closest possible approach of the incident particle?

1. $\frac{Z{e}^2}{2\pi {\epsilon }_{0}m{v}^2}$

2. $\frac{Ze}{4\pi {\epsilon }_{0}m{v}^2}$

3. $\frac{Z{e}^2}{8\pi {\epsilon }_{0}m{v}^2}$

4. $\frac{Ze}{8\pi {\epsilon }_{0}m{v}^2}$

Two charges q₁ and q₂ are placed 30 cm apart, as shown in the figure. A third charge q₃ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{q_3}{4\pi {\epsilon }_0}k$, where k is:

1. 8q₂

2. 8q₁

3. 6q₂

4. 6q₁

A charge of 10 e.s.u. is placed at a distance of 2 cm from a charge of 40 e.s.u. and 4 cm from another charge of 20 e.s.u. The potential energy of the charge 10 e.s.u. is: (in ergs) 

1. 87.5

2. 112.5

3. 150

4. 250

Four equal charges Q are placed at the four corners of a square of each side ‘a’. Work done in removing a charge – Q from its centre to infinity is:

1. 0

2. $\frac{\sqrt{2}{Q}^2}{4\pi {\epsilon }_{0}a}$

3. $\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$

4. $\frac{Q^2}{2\pi {\epsilon }_{0}a}$

Figure shows a ball having a charge q fixed at a point $\mathrm{A}$. Two identical balls having charges +q and –q and mass ‘m’ each are attached to the ends of a light rod of length $2\mathrm{a}$. The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid-point of the rod. The system is released from the situation as shown in the figure. The angular velocity of the rod when the rod becomes horizontal will be:

1. $\frac{\sqrt{2}\mathrm{q}}{3\mathrm{\pi }{\in }_0 {\mathrm{ma}}^3}$                         

2. $\frac{\mathrm{q}}{\sqrt{3\mathrm{\pi }{\in }_0 {\mathrm{ma}}^3}}$

3. $\frac{\mathrm{q}}{\sqrt{6\mathrm{\pi }{\in }_0 {\mathrm{ma}}^3}}$                       

4. $\frac{\sqrt{2}\mathrm{q}}{4\mathrm{\pi }{\in }_0 {\mathrm{ma}}^3}$

Three charges -Q, q, and -2Q are placed along a line as shown in the figure. The system of charges will have a positive potential energy configuration when q is placed at midpoint of line joining -Q and -2Q, if:
     

1. $q>\frac{Q}{3}$

2. $q<\frac{Q}{3}$

3. $q>\frac{-Q}{3}$

4. $q<\frac{-Q}{3}$