As per this diagram, a point charge \(+q\) is placed at the origin \(O.\) Work done in taking another point charge \(-Q\) from the point \(A,\) coordinates \((0,a),\) to another point \(B,\) coordinates \((a,0),\) along the straight path \(AB\) is:
1. | \( \left(\dfrac{-{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) | 2. | zero |
3. | \( \left(\dfrac{qQ}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \dfrac{1}{\sqrt{2}} \) | 4. | \( \left(\dfrac{{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) |
A network of four capacitors of capacity equal to is conducted to a battery as shown in the figure. The ratio of the charges on is:
1.
2.
3.
4.
The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:
1. | \(6~\mu\text{F}~\) | 2. | \(20~\mu\text{F} ~\) |
3. | \(3~\mu\text{F}~\) | 4. | \(10~\mu\text{F}\) |
1. | \(40\) V | 2. | \(10\) V |
3. | \(30\) V | 4. | \(20\) V |
A bullet of mass \(2\) g is having a charge of \(2\) µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10\) m/s?
1. \(50\) kV
2. \(5\) V
3. \(50\) V
4. \(5\) kV
1. | \(q\cdot E\) and \(p\cdot E \) |
2. | zero and minimum |
3. | \(q\cdot E\) and maximum |
4. | \(2q\cdot E\) and minimum |
1. | \(6 E,6 C\) | 2. | \( E,C\) |
3. | \(\frac{E}{6},6C\) | 4. | \(E,6C\) |
Some charge is being given to a conductor. Then it's potential:
1. | is maximum at the surface. |
2. | is maximum at the centre. |
3. | remains the same throughout the conductor. |
4. | is maximum somewhere between the surface and the centre. |
A capacitor of capacity \(C_1\) is charged up to \(V\) volt and then connected to an uncharged capacitor \(C_2\). Then final P.D. across each will be:
1. \(\frac{C_{2} V}{C_{1} + C_{2}}\)
2. \(\frac{C_{1} V}{C_{1} + C_{2}}\)
3. \(\left(1 + \frac{C_{2}}{C_{1}}\right)\)
4. \(\left(1 - \frac{C_{2}}{C_{1}} \right) V\)
If identical charges \((-q)\) are placed at each corner of a cube of side \(b\) then the electrical potential energy of charge \((+q)\) which is placed at centre of the cube will be:
1. | \(\dfrac{- 4 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\) | 2. | \(\dfrac{- 8 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}\) |
3. | \(\dfrac{- 4 q^{2}}{\sqrt{3} \pi\varepsilon_{0} b}\) | 4. | \(\dfrac{8 \sqrt{2} q^{2}}{4 \pi\varepsilon_{0} b}\) |