As shown in the figure, an electron is projec | vedclass

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

Question

(C) The electron is projected with kinetic energy $K = \frac{1}{2}mu^2$ at an angle $	heta = 45^\circ$ in a uniform electric field $E$ directed upwar

Vedclass · Accepted Answer

$\frac{K}{2qd}$

Vedclass · Answer

(C) The electron is projected with kinetic energy $K = \frac{1}{2}mu^2$ at an angle $	heta = 45^\circ$ in a uniform electric field $E$ directed upwards. The force on the electron is $F = qE$ downwards, so the acceleration is $a = \frac{qE}{m}$ downwards.The maximum vertical height $H$ reached by the electron is given by the formula for projectile motion: $H = \frac{u^2 \sin^2 	heta}{2a}$.Substituting the values $H = d$, $	heta = 45^\circ$, and $a = \frac{qE}{m}$:$d = \frac{u^2 \sin^2 45^\circ}{2(qE/m)}$Since $\sin 45^\circ = \frac{1}{\sqrt{2}}$, we have $\sin^2 45^\circ = \frac{1}{2}$.$d = \frac{u^2 (1/2)}{2qE/m} = \frac{mu^2}{4qE}$Given $K = \frac{1}{2}mu^2$, we can write $mu^2 = 2K$.Substituting this into the equation:$d = \frac{2K}{4qE} = \frac{K}{2qE}$Therefore, $E = \frac{K}{2qd}$.For the electron to strike the upper plate, the electric field must be such that the maximum height reached is at least $d$. Thus, $E$ must be greater than $\frac{K}{2qd}$.

As shown in the figure, an electron is projected with kinetic energy $K$ at an angle of $\theta = 45^\circ$ between two charged plates. The electron strikes the upper plate. The value of the electric field $E$ must be greater than:

Similar Questions

In Millikan's oil drop experiment,an oil drop of mass $16 \times 10^{-6} \ kg$ is balanced by an electric field of $10^6 \ V/m$. The charge in coulomb on the drop,assuming $g = 10 \ m/s^2$,is:

An electron with mass $9.1 \times 10^{-31} \ kg$ and charge $1.6 \times 10^{-19} \ C$ is placed in an electric field of $1 \times 10^6 \ V/m$. How much time will it take for the electron to reach a velocity equal to $1/10$th of the speed of light?

$A$ charge of magnitude $3e$ and mass $2m$ is moving in an electric field $\overrightarrow{E}$. The acceleration imparted to the charge is:

An oil drop having charge $2e$ is kept stationary between two parallel horizontal plates $2.0 \, cm$ apart when a potential difference of $12000 \, V$ is applied between them. If the density of oil is $900 \, kg/m^3$,the radius of the drop will be

Select the correct statement: (Only force on a particle is due to electric field)

Vedclass Test Series

Exam Paper Generator

Online Exam Module