Two identical metal plates are given charges $Q_1 and Q_2\left(<Q_1\right)$ respectively. If they are now brought close to form a parallel plate capacitor with capacitance $C$, the potential difference between them is :

1. $\frac{Q_1+Q_2}{2C}$

2. $\frac{Q_1+Q_2}{C}$

3. $\frac{Q_1-Q_2}{C}$

4. $\frac{Q_1-Q_2}{2C}$

An electron of mass m and charge e is accelerated from rest through a potential difference V in vacuum. The final speed of the electron will be 

(1) $V\sqrt{e/m}$

(2) $\sqrt{eV/m}$

(3) $\sqrt{2eV/m}$

(4) $2eV/m$

The electric potential at the surface of a charged solid sphere of insulator is 20V. The value of electric potential at its centre will be

1.  30V

2.  20V

3.  40V

4.  Zero

If E be the electric field inside a parallel plate capacitor due to Q and -Q charges on the two plates, then electrostatic force on plate having charge -Q due to the plate having charge +Q will be

1. -QE

2. $\frac{-QE}{2}$

3. QE

4. $\frac{-QE}{4}$

Two charged spheres of radii 10 cm and 15 cm are connected by a thin wire. No current will flow, if they have -

1. The same charge on each

2. The same potential

3. The same energy

4. The same field on their surfaces

In the electric field of a point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done

1. Is least along the path AB

2. Is least along the path AD

3. Is zero along all the paths AB, AC, AD and AE

4. Is least along AE

A conductor with a positive charge:

On rotating a point charge having a charge \(q\) around a charge \(Q\) in a circle of radius \(r,\) the work done will be:

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