If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10~\text {volts}\) to another point where the potential is \(\text{V volts}\), then the value of \(\mathrm{V}\) is:
1. \(5~\text {volts}\)
2. \(-15~\text {volts}\)
3. \(+15~\text {volts}\)
4. \(+10~\text {volts}\)

In a circuit, \(5~\text{C}\) of charge is passed through a battery in a given time. The plates of the battery are maintained at a potential difference of \(12~\text{V}.\) The work done by the battery is:

Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:

How much kinetic energy will be gained by an \(\alpha\text-\text{particle}\) in going from a point at \(70~\text{V}\) to another point at \(50~\text{V}\)?

Four point charges \(-Q, -q,2q~\text{and}~2Q\)$$ are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero, is:

A bullet of mass \(2~\text {gm}\) has a charge of \(2~\mu\text{C}.\) Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10~\text{m/s}?\)
1. \(50~\text {kV}\)
2. \(5~\text {V}\)
3. \(50~\text {V}\)
4. \(5~\text {kV}\)

The increasing order of the electrostatic potential energies for the given system of charges is given by:

Four electric charges \(+ q,\) \(+ q,\) \(- q\) and \(- q\) are placed at the corners of a square of side \(2L\) (see figure). The electric potential at the point \(A\), mid-way between the two charges \(+ q\) and \(+ q\) is:
              
1. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)\)
2. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)\)
3. zero
4. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)