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

1.	\(E\) at all points on the \(y\text-\)axis is along \(\hat i\)
2.	The electric field \(\vec E \) at all points on the \(x\text-\)axis has the same direction
3.	The dipole moment is \(2qd\) directed along \(\hat i\)
4.	The work has to be done to bring a test charge from infinity to the origin

A point charge of \(40~\text{stat coulomb }\)is placed \(2~\text{cm}\) in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is
1. \(100~\text{dynes}\)
2. \(160~\text{dynes}\)
3. \(1600~\text{dynes}\)
4. \(400~\text{dynes}\)

Four charges equal to – Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is 

1. $-\frac{Q}{4}(1+2\sqrt{2})$

2. $\frac{Q}{4}(1+2\sqrt{2})$

3. $-\frac{Q}{2}(1+2\sqrt{2})$

4. $\frac{Q}{2}(1+2\sqrt{2})$ 

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.

(1)
(2)

(3)
(4)

The electric field due to a uniformly charged solid sphere of radius R as a function of the distance from its centre is represented graphically by -

(1)  (2)

(3)  (4)

Two concentric conducting thin spherical shells \(A\) and \(B\) having radii \(r_A\) and \(r_B\) \((r_B>r_A)\) are charged to \(Q_A\) and $$\(-Q_B~(|Q_B|>|Q_A|).\) The electrical field at distance \(x\) from the common center is:

1.		2.
3.		4.

The electric field inside a spherical shell of uniform surface charge density is -

1. Zero

2. Constant, less than zero

3. Directly proportional to the distance from the centre

4. None of the above

The distance between charges 5 × 10^–11 C and –2.7 × 10^–11 C is 0.2 m. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is 

1. 0.44 m

2. 0.65 m

3. 0.556 m

4. 0.350 m

Suppose the charge of a proton and an electron differ slightly. One of them is \(\text- e\) and the other is \((e+\Delta e)\). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then $$\(\Delta e\) is of the order: [Given the mass of hydrogen, ${}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)]
1. \(10^{-20}~\text{C}\)
2. \(10^{-23}~\text{C}\)
3. \(10^{-37}~\text{C}\)
4. \(10^{-47}~\text{C}\)

Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d(d < < l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as:

1. \(v \propto x\)

2. \(v \propto x^{\frac{-1}{2}}\)

3. \(v \propto x^{-1}\)

4. \(v \propto x^{\frac{1}{2}}\)${\frac{\mathrm{}}{}}^{}$