# The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin cutting the axes at points $$\mathrm A$$, $$\mathrm B$$, $$\mathrm C$$ and $$\mathrm D$$ having coordinates $$(a,0),(0,a),(-a,0),(0,-a)$$ respectively. Out of the points on the periphery of the circle, the potential is minimum at: 1. $$\mathrm A$$ 2. $$\mathrm B$$ 3. $$\mathrm C$$ 4. $$\mathrm D$$

Subtopic:  Relation between Field & Potential |
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A thin, metallic spherical shell contains a charge $$\mathrm{Q}$$ on it. A point charge $$\mathrm{q}$$ is placed at the centre of the shell and another charge $$\mathrm{q}_1$$ is placed outside as it is shown in the figure. All the three charges are positive. The force on the charge at the centre is:

1. towards left
2. towards right
3. upward
4. zero

Subtopic:  Electrostatic Shielding |
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A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?

 (a) the electric field in the capacitor (b) the charge on the capacitor (c) the potential difference between the plates (d) the stored energy in the capacitor

Choose the correct option:
1. (a), (b)
2. (b) only
3. (c), (a)
4. (a), (d)

Subtopic:  Dielectrics in Capacitors |
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When the separation between two charges is increased, the electric potential energy of the charges:

 1 increases 2 decreases 3 remains the same 4 may increase or decrease

Subtopic:  Electric Potential Energy |
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A dipole ($$p$$) is placed so that it is always aligned along the x-axis but it can undergo displacement along the x-axis. The dipole is placed exactly midway between two fixed charges $$-Q$$ and $$Q,$$ in two possible ways.

Then, the dipole is:
 1 stable in both A, B 2 stable in A, unstable in B 3 unstable in A, stable in B 4 unstable in both A, B
Subtopic:  Energy of Dipole in an External Field |
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A positively charged light particle of charge $$q$$ and mass $$m$$ approaches another heavy particle of positive charge $$Q,$$ coming towards it with an initial speed $$u,$$ when it is far away.

The distance of the closest approach is given by:

1. $$\frac{q Q}{4 \pi \varepsilon_{0} m u^{2}}$$

2. $$\frac{q Q}{\pi \varepsilon_{0} m u^{2}}$$

3. $$\frac{q Q}{2 \pi \varepsilon_{0} m u^{2}}$$

4. $$\frac{4 \pi \varepsilon_{0} m u^{2}}{q Q}$$

Subtopic:  Electric Potential Energy |
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The $$6$$ $$\mu$$F capacitor is initially charged to $$2$$ V (i.e. $$V_B-V_A=2$$ V) while the $$3$$ $$\mu$$F capacitor is uncharged. The switch is now closed. The final potential difference across the $$3$$ $$\mu$$F capacitor will be:

1. $$4$$ V

2. $$\frac{4}{3}$$ V

3. $$2$$ V

4. $$\frac{8}{3}$$ V

Subtopic:  Capacitance |
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The left plate $$A$$ of an air capacitor is connected to the positive terminal while the right plate $$B$$ is connected to the negative terminal of a cell of voltage $$V_0.$$ Assume that the plate area is $$A,$$ and the plate separation is $$d.$$ If a slab of dielectric constant $$K$$ is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)

 1 more. 2 less. 3 equal. 4 more or less or equal depending on the value of $$K$$.
Subtopic:  Dielectrics in Capacitors |
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The equivalent capacitance of the circuit between the points $$A~\text{and}~B$$ is equal to:

1. $$2C$$
2. $$\frac{3C}{2}$$
3. $$3C$$
4. $$\frac{5C}{2}$$
Subtopic:  Combination of Capacitors |
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A charge is uniformly distributed on the circumference of a disc, and the potential at its centre is $$5$$ volt. If the charge was uniformly distributed on the surface of this disc, the potential at a point $$P$$ on its axis, at a distance equal to the disc's radius from its centre, equals:
1. $$10$$ V
2. $$5 \sqrt 2$$ V
3. $$10 \sqrt 2$$ V
4. $$10 (\sqrt {2} -1)$$ V