Two parallel disks each having radius R are separated by a distan… - Vidyadip

MCQ

Two parallel disks each having radius $R$ are separated by a distance $l$ . The surface charge densities are $\sigma $ and $-\sigma $ . The electric field at point $P$ , a large distance $r$ along the axis of the disks is

A
$\frac{{\sigma {R^2}l}}{{{\varepsilon _0}{r^3}}}$
B
$\frac{{2\sigma {R^2}l}}{{{\varepsilon _0}{r^3}}}$
C
$\frac{{\sigma {R^2}l}}{{4{\varepsilon _0}{r^3}}}$
✓
$\frac{{\sigma {R^2}l}}{{2{\varepsilon _0}{r^3}}}$

✓

Answer

Correct option: D.

$\frac{{\sigma {R^2}l}}{{2{\varepsilon _0}{r^3}}}$

d
Consider system of two disks to be short dipole.

$\mathrm{dE}=\frac{2 \mathrm{kdp}}{\mathrm{r}^{3}}$

$\mathrm{dp}=\mathrm{dq} \ell=\sigma \mathrm{d} \mathrm{A} \ell$

$\mathrm{E}=\frac{2 \mathrm{k}}{\mathrm{r}^{3}} \int \mathrm{dp}=\frac{2 \mathrm{k}}{\mathrm{r}^{3}} \ell \sigma \mathrm{A}$

${\rm{E}} = \frac{{2\ell }}{{4\pi { \in _0}{{\rm{r}}^3}}}\sigma \pi {{\rm{R}}^2} = \frac{{\sigma \ell {{\rm{R}}^2}}}{{2{ \in _0}{{\rm{r}}^3}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. Electric charges and fields→1. Electric charges and fields — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero

$(B)$ Potential at $B$ is zero

$(C)$ Charge is uniformly distributed on $A$

$(D)$ Charge is non uniformly distributed on $A$

When the key $K$ is pressed at time $t = 0$, which of the following statements about the current $I$ in the resistor $AB$ of the given circuit is true

Light of frequency $v$ falls on a material of threshold frequency $v_0$. Maximum kinetic energy of emitted electron is proportional to

Magnets A and B are geometrically similar but the magnetic moment of A is twice that of B. If $T_1$ and $T_2$ be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then $\frac{T_1}{T_2}$ will be

In the nuclear reaction $_{92}{U^{238}}{ \to _z}T{h^A}{ + _2}H{e^4}$, the values of $A$ and $Z$ are

The radius of a nucleus of mass number $64$ is $4.8$ fermi. Then the mass number of another nucleus having radius of $4$ fermi is $\frac{1000}{x}$, where $x$ is______.

A long straight wire carries a current of π amp. The magnetic field due to it will be $5 \times 10^{-5} weber/ \mathrm{m}^2$ at what distance from the wire [$\mu_0=$ permeability of air]

What is the equivalent resistance of the circuit ............. $\Omega$

Due to transitions among its first three energy levels, hydrogenic atom emits radiation at three discrete wavelengths $\lambda_1, \lambda_2$ and $\lambda_3\left(\lambda_1 < \lambda_2 < \lambda_3\right)$. Then,

In the figure shown, after the switch $‘S’$ is turned from position $‘A’$ to position $‘B’$, the energy dissipated in the circuit in terms of capacitance $‘C’$ and total charge $‘Q’$ is