Two equal charges q are placed at a distance of 2a and a third charge –2q is placed at the midpoint. The potential energy of the system is -

1. $\frac{q^2}{8\pi {\epsilon }_{0}a}$

2. $\frac{6q^2}{8\pi {\epsilon }_{0}a}$

3. $-\frac{7q^2}{8\pi {\epsilon }_{0}a}$

4. $\frac{9q^2}{8\pi {\epsilon }_{0}a}$

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is -

1. $qE{y}^2$

2. $q{E}^{2}y$

3. $qEy$

4. $q^{2}Ey$

How much kinetic energy will be gained by an $\alpha$– particle in going from a point at 70 V to another point at 50 V ?

1. $40eV$

2. $40keV$

3. $40MeV$

4. $0eV$

If a charged spherical conductor of radius 10 cm has potential V at a point distant 5 cm from its centre, then the potential at a point distant 15 cm from the centre will be -

1. $\frac{1}{3}V$

2. $\frac{2}{3}V$

3. $\frac{3}{2}V$

4. 3 V

An oil drop having charge 2e is kept stationary between two parallel horizontal plates 2.0 cm apart when a potential difference of 12000 volts is applied between them. If the density of oil is 900 kg/m³, the radius of the drop will be -

1. $2.0\times {10}^{-6}m$

2. $1.7\times {10}^{-6}m$

3. $1.4\times {10}^{-6}m$

4. $1.1\times {10}^{-6}m$

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of 100 volt is 

1. 1

2. $\sqrt{\frac{2m_e}{m_{\alpha }}}$

3. $\sqrt{\frac{m_e}{m_{\alpha }}}$

4. $\sqrt{\frac{m_e}{2m_{\alpha }}}$

When a proton is accelerated through 1V, then its kinetic energy will be -

1. 1840 eV

2. 13.6 eV

3. 1 eV

4. 0.54 eV

The displacement of a charge Q in the electric field $E=e_1\hat{i}+e_2\hat{j}+e_3\hat{k}$ is $\hat{r}=a\hat{i}+b\hat{j}$. The work done is 

1. $Q(a{e}_1+b{e}_2)$

2. $Q\sqrt{{\left(a{e}_1\right)}^2+{\left(b{e}_2\right)}^2}$

3. $Q(e_1+e_2)\sqrt{a^2+b^2}$

4. $Q\left(\sqrt{e_1^2+e_2^2)}\right(a+b)$