An infinite plane sheet of charge having unif | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The electric field due to an infinite plane sheet of charge is given by $E_S = \frac{|\sigma_s|}{2\epsilon_0}$.At the point $(0, 0, 2)$,the distan

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) The electric field due to an infinite plane sheet of charge is given by $E_S = \frac{|\sigma_s|}{2\epsilon_0}$.At the point $(0, 0, 2)$,the distance from the sheet (in the $x-y$ plane,i.e.,$z=0$) is $r_S = 2 	ext{ m}$.The electric field due to an infinitely long line charge is given by $E_{\ell} = \frac{|\lambda_e|}{2\pi\epsilon_0 r_{\ell}}$.The line charge is at $z=4 	ext{ m}$ and is parallel to the $y$-axis. The point is $(0, 0, 2)$. The perpendicular distance $r_{\ell}$ from the line charge to the point $(0, 0, 2)$ is $|4 - 2| = 2 	ext{ m}$.Given $|\sigma_s| = 2|\lambda_e|$.The ratio of the electric fields is:$\frac{E_S}{E_{\ell}} = \frac{|\sigma_s| / 2\epsilon_0}{|\lambda_e| / 2\pi\epsilon_0 r_{\ell}} = \frac{|\sigma_s|}{2\epsilon_0} 	imes \frac{2\pi\epsilon_0 r_{\ell}}{|\lambda_e|} = \frac{|\sigma_s| \pi r_{\ell}}{|\lambda_e|}$.Substituting the values $|\sigma_s| = 2|\lambda_e|$ and $r_{\ell} = 2 	ext{ m}$:$\frac{E_S}{E_{\ell}} = \frac{2|\lambda_e| 	imes \pi 	imes 2}{|\lambda_e|} = 4\pi$.We are given the ratio as $\pi \sqrt{n} : 1$,so $\pi \sqrt{n} = 4\pi$,which implies $\sqrt{n} = 4$.Therefore,$n = 16$.

Similar Questions

For a thin spherical shell of radius $R$ with a uniform surface charge density, which of the following graphs best represents the variation of the electric field magnitude $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the center?

$A$ total charge $q$ is divided into $q_1$ and $q_2$,which are placed at two vertices of an equilateral triangle of side $a$. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x = q_1 / q$. Choose the correct figure.

The time period of a block of mass $m$ suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $k$ is $T$ when the block is uncharged. If a charge $q$ is given to the block,what will be the new time period of oscillation?

In the following four situations,charged particles are at an equal distance from the origin. Arrange them in order of the magnitude of the net electric field at the origin,starting from the greatest.

Vedclass Test Series

Exam Paper Generator

Online Exam Module