The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance r(r > R) from its axis is 

(1) Directly proportional to r²

(2) Directly proportional to r³

(3) Inversely proportional to r

(4) Inversely proportional to r²

A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E 

(1) > F/q₀

(2) = F/q₀

(3) < F/q₀

(4) Cannot be estimated

The charge on \(500~\text{cc}\) of water due to protons will be: 

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is 

(1) ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{1/2}$

(2) ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{3/2}$

(3) ${\left(\frac{{\displaystyle I}}{{\displaystyle pE}}\right)}^{1/2}$

(4) ${\left(\frac{{\displaystyle p}}{{\displaystyle IE}}\right)}^{1/2}$

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. ${\in }_{o}A{a}^2$