Electrostatics - Electricity - Physics Previous Year Questions

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.

The electrostatic potential $\left(\phi_r\right)$ of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as

$$\begin{array}{ll} \phi_r=\frac{q}{4 \pi \epsilon_0 r} & \left(r \geq \mathrm{R}_0\right) \\ \phi_r=\frac{q}{4 \pi \epsilon_0 \mathrm{R}_0} & \left(r \leq \mathrm{R}_0\right) \end{array}$$

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

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

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

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 \((-a, 0,0)\) to \((0, a, 0)\) is

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\(^\circ\)

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 time constant as a function of time t is:

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 by \({Q \over {4\pi {\varepsilon _0}R}}\)

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 = 5a/4. Two points charges \(-\)7C and 3C are placed at (a/4, \(-\)a/4, 0) and (\(-\)3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces \(x=\pm a/2,y=\pm a/2,z=\pm a/2\). The electric flux through this cubical surface is

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 (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and \(\mu\) be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

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 given to the shells, \(Q_1:Q_2:Q_3\), is

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 \(r = R\), find the value of \(a\).