Electric Field Due to Disk and Infinitely Large Sheet

Q. Two infinite non-conducting sheets each with uniform surface charge density $\sigma$ are kept in such a way that the angle between them is ${30}^{\circ }$. The electric field in the region I shown between them is

1. $\frac{\sigma }{2{ϵ}_0}\left[\right(1+\sqrt{3})\hat{j}-\frac{\hat{i}}{2}]$
2. $\frac{\sigma }{2{ϵ}_0}\left[\right(1+\sqrt{3})\hat{j}+\frac{1}{2}\hat{i}]$
3. $\frac{\sigma }{{ϵ}_0}[(1+\frac{\sqrt{3}}{2})\hat{j}+\frac{1}{2}\hat{i}]$
4. $\frac{\sigma }{2{ϵ}_0}[(1-\frac{\sqrt{3}}{2})\hat{j}-\frac{\hat{i}}{2}]$

Q.

A square plate of side 2 m contains a charge uniformly distributed over one of its side, such that the surface charge density $\sigma$ is $10C/m^2$. The net charge on the square surface is n coulombs, where n is a natural number. The value of n is __.

Q.

The magnitude of electric field due to an infinite uniformly charged insulating sheet is 10 N/C at a point which is at a distance 3m away from it. The surface charge density of the sheet will be?

1. σ = 5ε₀ C/m2

2. σ = 20ε₀ C/m²

3. σ = ε₀ C/m²

4. None of these

Q.

Given a circular disk of radius R = 0.4 m and containing uniformly distributed charge with surface charge density, $\sigma =1C/m^2$. The electric field at a point P which is 0.3m along the axis of the disc from the centre is $\frac{1}{n{\epsilon }_0}$ where n is a natural number whose value is equal to ___

Q. The field due to a positively charged infinite sheet is perpendicularly out of the sheet.

1. False
2. True

Q. A proton is released from position near to positive plate. It reaches to opposite plate in time $t_1$, now one $\alpha$ particle is released & it reaches to opposite plate in time $t_2$, then $t_1:t_2$

1. $1:\sqrt{2}$
2. $1:1$
3. $1:2$
4. $2:1$

Q.
Electric field close to plane of charge is shown in figure. External electric field in V/m is

Q. A large conducting plate is placed between 2 positive charges $Q_1$ and $Q_2$.

1. $Q_1$ will be attracted towards plate
2. $Q_1$ will be repelled away from plate
3. There will be no net force on $Q_1$
4. net force on $Q_1$ will be away from $Q_2$

Q.
A neutral conducting rod is placed close to infinite charged plane then

1. Rod will be attracted towards plane.
2. Rod will be repulsed from plane
3. Net force on rod will be zero
4. Can't predict

Q. In a Van de Graaff electrostatic generator a rubber belt of 0.3 m width travels at a velocity of 20m/s. The belt is given a uniform surface charge at lower roller, so it produces a field of ${10}^{6}V/m$ in its vicinity. Current (in milliamperes) carried by the belt is