Three infinitely long charged sheets are plac | vedclass

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

Question

(A) The electric field due to an infinitely long charged sheet with surface charge density $\sigma$ is given by $\vec{E} = \frac{\sigma}{2\varepsilon_

Vedclass · Accepted Answer

$+\frac{2q\sigma}{\varepsilon_0} \hat{k}$

Vedclass · Answer

(A) The electric field due to an infinitely long charged sheet with surface charge density $\sigma$ is given by $\vec{E} = \frac{\sigma}{2\varepsilon_0} \hat{n}$,where $\hat{n}$ is the unit vector normal to the sheet pointing away from it.At point $P$ (located between $z=a$ and $z=2a$):$1$. Due to the sheet at $z=2a$ with charge density $+\sigma$: $\vec{E}_1 = -\frac{\sigma}{2\varepsilon_0} \hat{k}$ (directed downwards).$2$. Due to the sheet at $z=a$ with charge density $-2\sigma$: $\vec{E}_2 = -\frac{2\sigma}{2\varepsilon_0} \hat{k} = -\frac{\sigma}{\varepsilon_0} \hat{k}$ (directed towards the sheet,i.e.,downwards).$3$. Due to the sheet at $z=-a$ with charge density $-\sigma$: $\vec{E}_3 = -\frac{\sigma}{2\varepsilon_0} \hat{k}$ (directed towards the sheet,i.e.,downwards).The net electric field at $P$ is $\vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 = -\left(\frac{\sigma}{2\varepsilon_0} + \frac{\sigma}{\varepsilon_0} + \frac{\sigma}{2\varepsilon_0}\right) \hat{k} = -\frac{2\sigma}{\varepsilon_0} \hat{k}$.The electric force on charge $-q$ is $\vec{F} = (-q) \vec{E}_{net} = (-q) \left(-\frac{2\sigma}{\varepsilon_0} \hat{k}\right) = +\frac{2q\sigma}{\varepsilon_0} \hat{k}$.

Three infinitely long charged sheets are placed as shown in the figure. The electric force acting on a charge $-q$ placed at the point $P$ is ($\sigma=$ surface charge density,$\varepsilon_0=$ permittivity of free space).

Similar Questions

Obtain the expression for the electric field due to a straight wire of infinite length with a linear charge density $\lambda$.

An infinite line charge produces a field of $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. The linear charge density is . . . . . . . $\left(k = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right)$ (in $\text{ } \mu\text{C/m}$)

If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

$A$ sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre,for $x < R$,the electric field is directly proportional to

The total charge enclosed in an incremental volume of $2 \times 10^{-9} \, m^{3}$ located at the origin is ...... $nC$,if the electric flux density of its field is given by $\vec{D} = e^{-x} \sin y \hat{i} - e^{-x} \cos y \hat{j} + 2z \hat{k} \, C/m^{2}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module