Three charges –q₁, +q₂ and –q₃ are placed as shown in the figure. The x-component of the force on –q₁ is proportional to 

(1) $\frac{q_2}{b^2}-\frac{q_3}{a^2}\sin \theta$

(2) $\frac{q_2}{b^2}-\frac{q_3}{a^2}\cos \theta$

(3) $\frac{q_2}{b^2}+\frac{q_3}{a^2}\sin \theta$

(4) $\frac{q_2}{b^2}+\frac{q_3}{a^2}\cos \theta$

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-axis is along $\hat{i}$

(2) The electric field $\overrightarrow{E}$ at all points on the x-axis has the same direction

(3) Dipole moment is 2qd directed along $\hat{i}$

(4) Work has to be done in bringing a test charge from infinity to the origin

A point charge of 40 stat coulomb is placed 2 cm in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is

(1) 100 dynes

(2) 160 dynes

(3) 1600 dynes

(4) 400 dynes

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)

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:

(a) \(v \propto x\)

(b) \(v \propto x^{\frac{-1}{2}}\)

(c) \(v \propto x^{-1}\)

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

The electric field in a certain region is acting radially outward and is given by E=Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field will be given by

1. $4\pi {\in }_{o}A{a}^2$

2. $\pi {\in }_{o}A{a}^2$

3. $4\pi {\in }_{o}A{a}^3$

4. ${\in }_{o}A{a}^2$