Electrostatics Questions

A parallel plate air capacitor has capacity $C$, distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is:

In a region the potential is represented by $V(x,y,z)=6x-8xy-8y+6yz$, where $V$ is in volts and $x,y,z$ are in meters. The electric force experienced by a charge of $2\text{coulomb}$ situated at point $(1,1,1)$ is:

A conducting sphere of radius $R$ is given a charge $Q$. The electric potential and the electric field at the centre of the sphere respectively are:

Two thin dielectric slabs of dielectric constants $K_1$ and $K_2$ ($K_1<K_2$) are inserted between plates of a parallel plate capacitor. The variation of electric field '$E$ ' between the plates with distance '$d$ ' as measured from plate $P$ is correctly shown by:

$A,B$ and $C$ are three points in a uniform electric field $\vec{E}$ directed along the positive x-axis. $B$ is further left than $A$, and $A$ is further left than $C$. The electric potential is:

Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between them is $r$. Now the strings are rigidly clamped at half the height ($y/2$). The equilibrium separation between the balls now becomes:

Three concentric spherical shells have radii $a,b$ and $c$ ($a<b<c$) and have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively. If $V_A,V_B$ and $V_C$ denote the potentials of the three shells, then for $c=a+b$, we have:

Four point charges $-Q,-q,2q$ and $2Q$ are placed, one at each corner of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is:

An electric dipole of moment $\vec{p}$ is placed in an electric field of intensity $\vec{E}$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90^{\circ }$, the torque and the potential energy of the dipole will respectively be:

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$, the energy stored in the capacitor is:

Two metallic spheres of radii $1\text{cm}$ and $3\text{cm}$ are given charges of $-1\times 10^{-2}\text{C}$ and $5\times 10^{-2}\text{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

Charges $+q$ are at corners of isosceles $\Delta ABC$ (sides $BC=AC=2a$). $D,E$ are midpoints of $BC,CA$. Work done in moving $Q$ from $D$ to $E$ is:

Electric potential $V=4x^2\text{V}$. The electric field at $(1,0,2)$ is:

The electric potential at a point $(x,y,z)$ is given by $V=-x^{2}y-x{z}^3+4$. The electric field $\vec{E}$ at that point is:

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance $d(d\ll l)$ 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 spheres, as: