Electric field

The electric field $E$ is measured at a point $P(0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-I contains different relations between $E$ and $d$. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

The average current in the steady state registered by the ammeter in the circuit will be

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 μF and 9 μF capacitors), at a point distant 30 m from it, would equal :

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $-q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is(are)

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin O. In this distribution, a spherical cavity of radius $R_2$, centred at $P$ with distance $\mathrm{OP}=a=R_1-R_2$ (see figure) is made. If the electric field inside the cavity at position $\vec r$ is $\vec E(\vec r)$, then the correct statement(s) is(are)

A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge −σ 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 thin disc of radius b = 2a has a concentric hole of radius 'a' in it (see figure). It carries uniform surface charge 'σ' on it. If the electric field on its axis at height 'h' (h<<a) from its centre is given as 'Ch' then value of 'C' is :

A wire, of length L(=20 cm), is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges ±Q, [|Q| = $10^3\epsilon_0$ Coulomb where $\epsilon_0$ is the permittivity (in SI units) of free space] the net electric field at the centre O of the semi-circular arc would be :

Let $E_1(r)$, $E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0)=E_2(r_0)=E_3(r_0)$ at a given distance $r_0$, then

Charges $Q$, $2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii $R/2$, $R$ and $2R$, respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the center of spheres 1, 2 and 3 are $E_1$, $E_2$ and $E_3$ respectively, then

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 $V_A$ the potential at $x=2$ m is :

Two non-conducting solid spheres of radii $R$ and $2R$, having uniform volume charge densities $\rho_1$ and $\rho_2$ respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio $\dfrac{\rho_1}{\rho_2}$ can be

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then $X$ is nearly

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K=\dfrac1{4\pi\varepsilon_0}\dfrac q{L^2}$, which of the following statement(s) is(are) correct?

A wooden block performs SHM on a frictionless surface with frequency, $\nu_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\vec E$ is switched-on as shown, then the SHM of the block will be

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 tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\dfrac{81\pi}{7}\times10^5$ V m⁻¹. When the field is switched off, the drop is observed to fall with terminal velocity $2\times10^{-3}$ m s⁻¹. Given $g=9.8$ m s⁻², viscosity of the air $=1.8\times10^{-5}$ N s m⁻² and the density of oil $=900$ kg m⁻³, the magnitude of $q$ 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.

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