Electric Potential Due to Charged Infinite Sheets

Q.
A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances $r$ & $2r$ respectively, if energy (electrostatic) stored in them are $U_A$ & $U_B$ respectively then,

1. $U_A:U_B=4:1$
2. $U_A:U_B=1:1$
3. $U_A:U_B=1:4$
4. $U_A:U_B=8:1$

Q. The electric potential due to a uniform disc of surface charge density $0.5C/m^2$ and radius 3 cm, at a point 4 cm from the centre on its perpendicular axis is

1. $4{\epsilon }_0$
2. $8{\epsilon }_0$
3. $\frac{1}{4{\epsilon }_0}$
4. $\frac{1}{8{\epsilon }_0}$

Q. Quarter non-conducting disc of radius 4R having uniform surface charge density $\sigma$ is placed in xz-plane, then which of the following is correct?

1. Electric potential at $(0,3R,0)is\frac{\sigma R}{4{ϵ}_0}$
2. Electric potential at $(0,0,0)\text{is}\frac{\sigma R}{2{ϵ}_0}$
3. Electric field at (0, 3R, 0) is symmetric with x and z axis
4. Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis

Q.

The potential difference between two oppositely charged infinite sheets, with charge density σ and separation D, is proportional to?

​

1. 1/σ

2. σ

3. 1/D

4. $\frac{1}{D^2}$

Q. Assuming reference point (for calculating electric potential) to be at infinity, mark the correct statement(s)

1. Electric potential at the centre of a uniformly charged spherical shell due to its own charge is zero.
2. Electric potential at the centre of a uniformly charged sphere due to its own charge is zero.
3. Self energy of a dipole is positive.
4. If we change the reference point, the potential difference between 2 points will not change.

Q. A charge of -5C is brought closer to a positively charged infinite sheet of uniform charge density. The work done by the field is .

1. Positive
2. Negative
3. Zero
4. Infinte

Q. The electric potential due to a uniform disc of surface charge density $0.5C/m^2$ and radius 3 cm, at a point 4 cm from the centre on its perpendicular axis is

1. $4{\epsilon }_0$
2. $8{\epsilon }_0$
3. $\frac{1}{4{\epsilon }_0}$
4. $\frac{1}{8{\epsilon }_0}$

Q.
A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances $r$ & $2r$ respectively, if energy (electrostatic) stored in them are $U_A$ & $U_B$ respectively then,

1. $U_A:U_B=4:1$
2. $U_A:U_B=1:1$
3. $U_A:U_B=1:4$
4. $U_A:U_B=8:1$