An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like 

(1) A

(2) B

(3) C

(4) D

The magnitude of electric field E in the annular region of a charged cylindrical capacitor 

(1) Is same throughout

(2) Is higher near the outer cylinder than near the inner cylinder

(3) Varies as 1/r, where r is the distance from the axis

(4) Varies as 1/r², where r is the distance from the axis

A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as 

1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests 

(1) E_A > E_B > E_C

(2) E_A = E_B = E_C

(3) E_A = E_C > E_B

(4) E_A = E_C < E_B

A hollow insulated conducting sphere is given a positive charge of 10μC. What will be the electric field at the centre of the sphere if its radius is 2 meters 

(1) Zero

(2) 5 μCm^–2

(3) 20 μCm^–2

(4) 8 μCm^–2

An electron of mass \(m_{e}\) initially at rest, moves through a certain distance in a uniform electric field in time \(t_{1}.\) A proton of mass \(m_{p}\) also initially at rest takes time \(t_{2}\) to move through an equal distance in this uniform electric field. The ratio of \(\frac{t_{2}}{t_{1}}\) is nearly equal to- (Neglect the effect of gravity.)

1. \(1\)
2. \(\left ( \frac{m_{p}}{m_{e}} \right )^{1/2}\)
3. \(\left ( \frac{m_{e}}{m_{p}} \right )^{1/2}\)
4. \(1836\)

Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then:

(1) only -q is in stable equilibrium.

(2) none of the charges are in equilibrium.

(3) all the charges are in unstable equilibrium.

(4) all the charges are in stable equilibrium.

Three identical positive point charges, as shown are placed at the vertices of an isosceles right-angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point \(M\) of the hypotenuse?
                 
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

The figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?

(1) 1

(2) 2

(3) 3

(4) 4