The figure shows the electric lines of force emerging from a charged body. If the electric field at \(A\) and \(B\) are \(E_A\) and \(E_B\) respectively and if the displacement between \(A\) and \(B\) is \(r,\) then:

        

1. \(E_A>E_B\)

2. \(E_A<E_B\)

3. $E_A=\frac{E_B}{r}$

4. $E_A=\frac{E_B}{r^2}$

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

1. 1

2. 2

3. 3

4. 4

X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B, and C are as shown in the figure. The incorrect option is:

Three charges are placed at the vertices of an equilateral triangle of side \(a\) as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is: 

1. $Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

2. $-Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

3. zero

4. $Q^2/\left(2\pi {\epsilon }_0{a}^2\right)$

Two identical conductors of copper and aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminium will be:

1. zero.

2. greater than in copper.

3. equal to that in copper.

4. less than in copper.

The charge on 500 cc of water due to protons will be: 

Two-point charges, +q and –q are held fixed at (–d, 0) and (d, 0) respectively of an (x, y) coordinate system. Then: 

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in:

1.		2.
3.		4.

Which of the following graphs shows the variation of electric field \(E\) due to a hollow spherical conductor of radius \(R\) as a function of distance from the centre of the sphere?

1.		2.
3.		4.

Two-point charges +8q and –2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is:

1. 8L

2. 4L

3. 2L

4. $\frac{L}{4}$