There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60^o with the direction of the field ?

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu $$C charge, its radius will be :
[ Take : $${1 \over {4\,\pi { \in _0}}} = $$ 9 $$ \times $$ 10⁹ N $$-$$ m²/C² ]

An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to $$ . The angle $$\theta$$ is:

Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V₀, V₀ + $$\Delta $$V, V₀ + 2$$\Delta $$V, .......... V₀ + N$$\Delta $$V ($$\Delta $$ V > 0), are drawn and have increasing radii r₀, r₁, r₂,..........r_N, respectively. If the difference in the radii of the surfaces is constant for all values of V₀ and $$\Delta $$V then :