An electron is projected towards a metal plat | vedclass

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

Question

(D) The electric field $E$ near a charged conducting plate is given by $E = \frac{|\sigma|}{\in_0}$.The force on the electron is $F = eE = e \frac{|\s

Vedclass · Accepted Answer

$\frac{E_k \in_0}{e\sigma}$

Vedclass · Answer

(D) The electric field $E$ near a charged conducting plate is given by $E = \frac{|\sigma|}{\in_0}$.The force on the electron is $F = eE = e \frac{|\sigma|}{\in_0}$.Since the electron is moving against the electric field (repelled by the negative plate),the work done by the electric field is negative,or the work done by the external kinetic energy to reach the plate is equal to the change in potential energy.Using the work-energy theorem,the initial kinetic energy $E_k$ is completely converted into work done against the electric force over distance $d$:$E_k = F \cdot d = (eE) \cdot d$Substituting $E = \frac{|\sigma|}{\in_0}$:$E_k = e \left( \frac{|\sigma|}{\in_0} \right) d$Solving for $d$:$d = \frac{E_k \in_0}{e|\sigma|}$Given the magnitude of charge density is $|\sigma|$,the expression matches option $D$.

An electron is projected towards a metal plate with a surface charge density $\sigma = -2 \times 10^{-6} \ C/m^2$. If the electron strikes the plate with zero velocity,calculate the distance $d$ between the electron gun and the plate in terms of its initial kinetic energy $E_k$.

Similar Questions

The electric field intensity on the surface of a solid charged sphere of radius $r$ and volume charge density $\rho$ is ( $\epsilon_0=$ permittivity of free space).

What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.

$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

The electric field in a region is radially outward with magnitude $E = A r_0$. The charge contained in a sphere of radius $r_0$ centered at the origin is

For two infinitely long charged parallel sheets with the same surface charge density $\sigma$,the electric field at point $P$ between them is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module