Four particles each having charge q are placed at the vertices of a square of side a. The value of the electric potential at the midpoint of one of the side will be

1.  0

2.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(2+\frac{2}{\sqrt{5}})$

3.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(2-\frac{2}{\sqrt{5}})$

4.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(1+\frac{1}{\sqrt{5}})$

A metallic sphere of capacitance $C_1$, charged to electric potential $V_1$ is connected by a metal wire to another metallic sphere of capacitance $C_2$ charged to electric potential $V_2$. The amount of heat produced in connecting the wire during the process is:

1.$\frac{C_1{C}_2}{2\left(C_1+C_2\right)}{\left(V_1+V_2\right)}^2$

2. $\frac{C_1{C}_2}{2(C_1+C_2)}{(V_1-V_2)}^2$

3. $\frac{C_1{C}_2}{C_1+C_2}{(V_1-V_2)}^2$

4. zero

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

The capacitance of a parallel plate capacitor is C. If a dielectric slab of thickness equal to one-fourth of the plate separation and dielectric constant K is inserted between the plates, then new capacitance become

1. $\frac{KC}{2\left(K+1\right)}$

2. $\frac{2KC}{K+1}$

3. $\frac{5KC}{4K+1}$

4. $\frac{4KC}{3K+1}$

The electric potential at a point at distance 'r' from a short dipole is proportional to

1. $r^2$

2. ${\mathrm{r}}^{-1}$

3. $r^{-2}$

4. $r^1$

You are traveling in a car during a thunderstorm. In order to protect yourself from lightning, you would prefer to

1. Touch the nearest electric pole

2. Take shelter under a tree

3. Get out and crouch on the ground

4. Remain in the car

Capacitors $C_1=10\mu F and C_2=30\mu F$ are connected in series across a source of emf 20KV. The potential difference across $C_1$ will be

1. 5 KV

2. 15 KV

3. 10 KV

4. 20 KV

Two metallic spheres of radii 2cm and 3cm are given charges 6mC and 4mC respectively. The final charge on the smaller sphere will be if they are connected by a conducting wire

1. 4mC

2.6mC

3. 5mC

4. 10mC