Electrostatics — JEE Main PYQs

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is:

Three charges $+\mathrm{Q},\mathrm{q},+\mathrm{Q}$ are placed respectively, at distance, $0,\mathrm{d}/2$ and d from the origin, on the $x$-axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then value of $q$ is

A uniformly charged ring of radius $3a$ and total charge $q$ is placed in $xy$-plane centered at origin. A point charge q is moving towards the ring along the z-axis and has speed v at $z=4a$. The minimum value of $v$ such that it crosses the origin is:

Three concentric metal shells A, B and C of respective radii $a,b$ and $c$ ($a<b<c$) have surface charge densities $+\sigma ,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :

An electric dipole has a fixed dipole moment $\overrightarrow{\mathrm{p}}$, which makes angle $\theta$ with respect to $x$-axis. When subjected to an electric field ${\overrightarrow{\mathrm{E}}}_1=\mathrm{E}\hat{i}$, it experiences a torque …

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such th …

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

A uniformly charged solid sphere of radius R has potential V0 (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials 3V0/2, 5V0/4, 3V0/4 and V0/4 have radius R1, R2, R3 and R4 respectively. Then: [options — see source PDF]

Assume that an electric field $\vec{E}=30x^2\hat{i}$ exists in space. Then the potential difference $V_A-V_O$, where $V_O$ is the potential at the origin and ${\mathrm{V}}_{\mathrm{A}}$ the potential at $\mathrm{x}=2\mathrm{m}$ is:

Two charges, each equal to q , are kept at $\mathrm{x}=-\mathrm{a}$ and $\mathrm{x}=\mathrm{a}$ on the x -axis. A particle of mass m and charge ${\mathrm{q}}_0=\frac{\mathrm{q}}{2}$ is placed at the origin. If charge ${\mathrm{q}}_0$ is given a small displacement ( …

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:

In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distri …

Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance $d(d\ll l)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each …

The electrostatic potential inside a charged spherical ball is given by $\varphi =\alpha r^2+b$ where $r$ is the distance from the centre; $a,b$ are constants. Then the charge density inside ball is

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\overrightarrow{\mathrm{E}}$ at the centre O is

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)={\rho }_0\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho (r)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r(r<R)$ f …

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8{\text{g cm}}^{-3}$, the angle remains the same. If density of the material of the sphere is …

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - 1: For a charged particle moving from point P to point Q , the net work done by an electrostatic field on the par …

Let $P(r)=\frac{Q}{\pi R^4}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. for a point ' $p$ ' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

Two points P and Q are maintained at the potentials of 10 V and -4 V respectively. The work done in moving 100 electrons from $P$ to $Q$ is

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on Q is zero, then the $\mathrm{Q}/\mathrm{q}$ equals

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-I:
For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its s …

A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0\le r<\infty$, where $r$ is the distance from the centre of the shell?

An electric charge $10^{-3}\mu C$ is placed at the origin $(0,0)$ of X-Y co-ordinate system. Two points A and B are situated at $(\sqrt{2},\sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points A and B will be

If $g_E$ and $g_m$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio …

Charges are placed on the vertices of a square as shown. Let $\vec{E}$ be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

The potential at a point x (measured in $\mu$m) due to some charges situated on the x-axis is given by $V(x)=\frac{20}{x^2-4}$ volts. The electric field E at $x=4\mu$m is given by

A electric dipole is placed at an angle of $30^{\circ }$ to a non-uniform electric field. The dipole will experience

An alpha nucleus of energy $\frac{1}{2}m{v}^2$ bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

Two spherical conductors $A$ and $B$ of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres …

A charged ball $B$ hangs from a silk thread $S$ which makes an angle $\theta$ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$ axis at which the net electric field due to these two point charges is zero is

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q$. The potential difference between the centres of the two rings is

Two spherical conductor B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged brought in contact with B, then brought in contact wit …

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium the value of $q$ is

A charged oil drop is suspended in a uniform field of $3\times 10^4\mathrm{V}/\mathrm{m}$ so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge $=9.9\times 10^{-15}\mathrm{kg}$ and $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)