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

An infinite number of electric charges each equal to 5 nC (magnitude) are placed along the x-axis at x = 1 cm, x = 2 cm, x = 4 cm, x = 8 cm ………. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at x = 0 is: $\left(\frac{{\displaystyle 1}}{{\displaystyle 4\pi {\epsilon }_0}}=9\times {10}^{\mathrm{9 }}N-m^2/C^2\right)$

1. 12 × 10⁴

2. 24 × 10⁴

3. 36 × 10⁴

4. 48 × 10⁴

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

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 $-Q_B\left(\right|Q_B|>|Q_A\left|\right)$. 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