Electrostatics

A tiny spherical oil drop carrying a net charge \(q\) is balanced in still air with a vertical uniform electric field of strength \({{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.\) When the field is switched off, the drop is observed to f...

A uniformly charged thin spherical shell of radius \(R\) carries uniform surface charge density of \(\sigma\) per unit area. It is made of two hemispherical shells, held together by pressing them with force \(F\) (see figure). \(F\) is pro...

A few electric field lines for a system of two charges \({Q_1}\) and \({Q_2}\) fixed at two different points on the \(x\)-axis are shown in the figure. These lines suggest that

A solid sphere of radius R has a charge Q distributed in its volume with a charge density \(\rho = K{r^a}\), where K and a are constants and r is the distance from its centre. If the electric field at \(r = R/2\) is 1/8 times than at $$r =...

Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (...

Three concentric metallic spherical shells of radii \(R,2R,3R\) are given charges \(Q_1,Q_2,Q_3\), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges giv...

A disk of radius \({a \over 4}\) having a uniformly distributed charge 6C is placed in the xy-plane with its centre at (\(-\)a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x ...

The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

For a = 0, the value of d (maximum value of \(\rho\) as shown in the figure) is

The electric field at r = R is :

STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given ...

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is \(\frac{d}{3}\) initially. Suppose the liquid level decreases at a constant speed V, the tim...

Consider a system of three charges \({q \over 3},{q \over 3}\) and \(- {{2q} \over 3}\) placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60\(^\circ\)

Positive and negative point charges of equal magnitude are kept at \(\left(0,0, \frac{a}{2}\right)\) and \(\left(0,0, \frac{-a}{2}\right)\), respectively. The work done by the electric field when another positive point charge is moved from ...

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinder are initially electrically neutral.

The electrostatic potential $\left(\phi_r\right)$ of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as
$$ \begin{array}{ll} \phi_r=\frac{q}{4 \pi \epsilon_0 r} & \left(r \geq \mathrm{R}_0\right) \\ ...

A conducting liquid bubble of radius \(a\) and thickness \(t(t < < a)\) is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet.