A large flat metal surface has a uniform charge density $\left(+ \sigma\right)$ . An electron of mass~ $m$ and charge $ρ$ leaves the surface at the point~ $A$ with speed~ $u$ and returns to it at point $B$ . Disregarding gravity the maximum value of $AB$ is

Question

A large flat metal surface has a uniform charge density

\left(+ \sigma\right)

. An electron of mass~

m

and charge

ρ

leaves the surface at the point~

A

with speed~

u

and returns to it at point

B

. Disregarding gravity the maximum value of

AB

is

A large flat metal surface has a uniform charge density (+ σ) . An electron of mass~ m and charge ρ leaves the surface

Quantrex Academy · Accepted Answer

Correct answer: C. 2 ε _ 0 mu^ 2 ρσ

Electric field due to one surface of the large metal plate,

A large flat metal surface has a uniform charge density (+ σ) . An electron of mass~ m and charge ρ leaves the surface

The projected electron's motion will be on a curved path like a projectile.

∴

AB will be maximum when

\theta = 45 °

Range

A{B}_\max = \dfrac{u^{2}}{a}

a = \dfrac{ρE}{m} = \dfrac{ρ\sigma}{2{ε}_{0}m}

= \dfrac{u^{2}}{\dfrac{ρ\sigma}{2{ε}_{0}m}} = \dfrac{2{ε}_{0}mu^{2}}{ρ\sigma}

A large flat metal surface has a uniform charge density (+ σ) . An...

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