Electrostatics Questions

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:

Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is $q$ and the force of repulsion between them is $F$. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (Radii of A and B are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as:

An electric dipole with dipole moment $5\times 10^{-6}\text{Cm}$ is aligned with the direction of a uniform electric field of magnitude $4\times 10^5\text{N/C}$. The dipole is then rotated through an angle of $60^{\circ }$ with respect to the electric field. The change in the potential energy of the dipole is:

The plates of a parallel plate capacitor are separated by $d$. Two slabs of different dielectric constant $K_1$ and $K_2$ with thickness $\frac{3}{8}d$ and $\frac{d}{2}$, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If $K_1=1.25K_2$, the value of $K_1$ is:

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4πε0)k, where k is :

A charge $Q$ is enclosed by a Gaussian spherical surface of radius $R$. If the radius is doubled, then the outward electric flux will:

Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2L$. The electric potential at point $A$, midway between the two charges $+q$ and $+q$, is:

A parallel plate condenser has a uniform electric field $E$ (V/m) in the space between the plates. If the distance between the plates is $d$ (m) and area of each plate is $A$ ($m^2$), the energy (joules) stored in the condenser is:

A capacitor of $2\mu \text{F}$ is charged as shown in the diagram. When the switch $S$ is turned to position 2, the percentage of its stored energy dissipated is:

If potential (in volts) in a region is expressed as $V(x,y,z)=6xy-y+2yz$, the electric field (in N/C) at point $(1,1,0)$ is:

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:

What is the flux through a cube of side ‘$a$ ’ if a point charge of $q$ is at one of its corners?

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:

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:

An electric dipole is placed at an angle of $30^{\circ }$ with an electric field intensity $2\times 10^5\text{N/C}$. It experiences a torque equal to $4\text{N m}$. The charge on the dipole, if the dipole length is $2\text{cm}$, is:

A parallel-plate capacitor of area $A$, separation $d$ and capacitance $C$ is filled with four dielectric materials as shown. If a single dielectric material is to be used to have the same capacitance $C$, then its dielectric constant $k$ is:

A hollow cylinder has a charge $q$ coulomb within it (at the geometrical centre). If $\varphi$ is the electric flux associated with the curved surface $B$, the flux linked with the plane surface $A$ is:

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge - Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is :

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4πε 0)k, where k is :

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge - Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is :

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4πε0)k, where k is :

Two infinitely long parallel conducting plates having surface charge densities $+\sigma$ and $-\sigma$ respectively, are separated by a small distance. The medium between the plates is vacuum. If ${\epsilon }_0$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:

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 $-Q_B$ ($|Q_B|>|Q_A|$). The electrical field along a line (passing through the centre) is:

Four point $+ve$ charges of same magnitude ($Q$) are placed at four corners of a rigid square frame as shown in figure. The plane of the frame is perpendicular to $Z$ -axis. If a $-ve$ point charge is placed at a distance $z$ away from the above frame ($z\ll L$) then:

Three-point charges $+q$, $-2q$ and $+q$ are placed at points $(0,a,0)$, $(0,0,0)$ and $(a,0,0)$, respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

Two condensers, one of capacity $C$ and the other of capacity $C/2$ are connected to a $V$ volt battery, as shown. The work done in charging fully both the condensers 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:

Charges $+q$ and $-q$ are placed at points $A$ and $B$, respectively; distance $2L$ apart. $C$ is the midpoint. The work done in moving a charge $+Q$ along the semicircle $CRD$ is:

The energy required to charge a parallel plate condenser of plate separation $d$ and plate area of cross-section $A$ such that the uniform electric field between the plates is $E$, is:

A thin conducting ring of radius $R$ is given a charge $+Q$. The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E$. The electric field at the centre due to the charge on the part $ACDB$ of the ring is:

The electric potential at a point in free space due to a charge $Q$ coulomb is $Q\times 10^{11}$ volts. The electric field at that point is:

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:

Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will be:

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:

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