A thin spherical conducting shell of radius \(R\) has a charge \(q.\) Another charge \(Q\) is placed at the centre of the shell. The electrostatic potential at a point \(P\) which is at a distance \(\frac{R}{2}\) from the centre of the shell is:
1. \(\frac{\left( q + Q \right)}{4 \pi \varepsilon_{0}} \frac{2}{R}\)
2. \(\frac{2 Q}{4 \pi \varepsilon_{0} R}\)
3. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} - \frac{2 q}{4 \pi \varepsilon_{0} R}\)
4. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} + \frac{q}{4 \pi \varepsilon_{0} R}\)
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. | \(250\) |
In a certain charge distribution, all points having zero potential can be joined by a circle \(S\). Points inside \(S\) have positive potential, and points outside \(S\) have a negative potential. A positive charge, which is free to move, is placed inside \(S\). What is the correct statement about \(S\):
1. | It will remain in equilibrium | 2. | It can move inside \(S\), but it cannot cross \(S\) |
3. | It must cross \(S\) at some time | 4. | It may move, but will ultimately return to its starting point |
Two charges \(q_1\) and \(q_2\) are placed \(30~\text{cm}\) apart, as shown in the figure. A third charge \(q_3\) is moved along the arc of a circle of radius \(40~\text{cm}\) from \(C\) to \(D.\) The change in the potential energy of the system is \(\dfrac{q_{3}}{4 \pi \varepsilon_{0}} k,\) where \(k\) is:
1. | \(8q_2\) | 2. | \(8q_1\) |
3 | \(6q_2\) | 4. | \(6q_1\) |
If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).
Three capacitors of capacitances \(3~\mu\text{F}\), \(9~\mu\text{F}\) and \(18~\mu\text{F}\) are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases \(\frac{C_s}{C_p}\) will be:
1. \(1:15\)
2. \(15:1\)
3. \(1:1\)
4. \(1:3\)
Four capacitors each of capacity \(3~\mu\text{F}\) are connected as shown in the adjoining figure. The ratio of equivalent capacitance between \(A\) and \(B\) and between \(A\) and \(C\) will be:
1. \(4:3\)
2. \(3:4\)
3. \(2:3\)
4. \(3:2\)
A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \(A\) metre2 and the separation is \(t\) metre. The dielectric constants are \(k_1\) and \(k_2\) respectively. Its capacitance in farad will be:
1. \(\frac{\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
2. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} + k_{2}\right)}{2}\)
3. \(\frac{2\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
4. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} - k_{2}\right)}{2}\)
In the connections shown in the adjoining figure, the equivalent capacity between \(A\) and \(B\) will be:
1. \(10.8~\mu\text{F}\)
2. \(69~\mu\text{F}\)
3. \(15~\mu\text{F}\)
4. \(10~\mu\text{F}\)
The diagrams below show regions of equipotentials.
1. | the maximum work is required to move \(q\) in figure(iii). |
2. | in all four cases, the work done is the same. |
3. | the minimum work is required to move \(q\) in the figure(i). |
4. | the maximum work is required to move \(q\) in figure(ii). |