Two-point charges, \(+q\) and \(-q\) are held fixed at \((-d,0)\) and \((d,0)\) respectively of an \((x,y)\) 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.	Dipole moment is \(2qd\) directed along \(\hat i.\)
4.	Work has to be done in bringing a test charge from infinity to the origin.

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

(1)  (2)

(3)  (4)

Suppose the charge of a proton and an electron differ slightly. One of them is -e and the other is $\left(e+∆e\right)$. If the net of electrostatic force and gravitaional force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero,then $∆e$ is of the order [Given mass of hydrogen, $m_h$=1.67$\times {10}^{-27}$ kg]

(a) ${10}^{-20}C$

(b)${10}^{-23}C$

(c) ${10}^{-37}C$

(d) ${10}^{-47}C$

An electric dipole is place at an angle of ${30}^{\circ }$ with an electric field intensity 2$\times {10}^5$ N/C. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is

(a) 8 mC              (b) 2 mC

(c) 5 mC              (d) 7 $\mu$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)$v \alpha x$ 

(b)$v \alpha x^{\frac{-1}{2}}$

(c)$v \alpha x^{-1}$

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

 

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. ${\in }_{o}A{a}^2$

What is the flux through a cube of side a if a point charge of q is a one of its corner?

1. $\frac{2q}{{\epsilon }_0}$                                         

2. $\frac{q}{8{\epsilon }_0}$

3. $\frac{q}{{\epsilon }_0}$                                         

4. $\frac{q}{2{\epsilon }_0}6a^2$

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

1. be reduced to half                                 

2. remain the same

3. be doubled

4. increase four times

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

1. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2 }{e^2}$                  2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fe}}^2}{d^2}}$

3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{e^2}}$               4. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{q^2}$

A surface of side L metre in the plane of the paper is placed in a uniform electric field E(volt/m) acting along the same place at an angle $\theta$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of V-m, is

(a) EL²                (b) EL²cos$\theta$

(c) EL²sin$\theta$          (d) 0