The electric field at a distance $\frac{3\mathrm{R}}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{\mathrm{R}}{2}$ from the centre of the sphere is 

1. $\mathrm{zero}$                                     2. $E$

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

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is 

1. 3E along KO 

2. E along OK 

3. E along KO

4. 3E along OK  

There is a uniform electric field of strength \(10^3\) V/m along the y-axis. A body of mass \(1\) g and charge \(10^{-6}\) C is projected into the field from the origin along the positive x-axis with a velocity \(10\) m/s. Its speed in m/s after \(10\) s is (neglect gravitational effects) 
1. \(10\)
2. \(5\sqrt{2}\)
3. \(10\sqrt{2}\)
4. \(20\)

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q, R, S, T and U respectively 

(1) +, –, +, –, –, +

(2) +, –, +, –, +, –

(3) +, +, –, +, –, –

(4) –, +, +, –, +, –

A charge of magnitude 3e and mass 2m is moving in an electric field E. The acceleration imparted to the charge is

(1) 2Ee / 3m                 

(2) 3Ee / 2m 

(3) 2m / 3Ee                 

(4) 3m / 2Ee

Two parallel metal plates having charges +Q and -Q faces each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

1. become zero                                   

2. increase

3. decrease                                         

4. remain same

A surface of side L metre in the plane of the paper is placed in a uniform electric field E(volt/m) acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of V-m, is

(1) EL² 

(2) EL²cos$\theta$

(3) EL²sin$\theta$

(4) 0

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

1. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2 }{e^2}$                  2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fe}}^2}{d^2}}$

3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{e^2}}$               4. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{q^2}$

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

1. be reduced to half                                 

2. remain the same

3. be doubled

4. increase four times

What is the flux through a cube of side 'a' if a point charge q is at one of its corners?

1. $\frac{2q}{{\epsilon }_0}$                                         

2. $\frac{q}{8{\epsilon }_0}$

3. $\frac{q}{{\epsilon }_0}$                                         

4. $\frac{q}{2{\epsilon }_0}6a^2$