Question

A proton beam passes without deviation through a region of space where there are uniform transverse mutually perpendicular electric and magnetic field $E$ and $B$ . Then the beam strikes a grounded target. The force imparted by the beam on the target if the beam current is equal to $I$ is

• A. $\frac{\text{mEI}}{\text{eB}}$
• B. $\frac{\text{mIE}}{\text{e}}$
• C. $\frac{\text{mEI}}{\text{B}}$
• D. $\frac{\text{eIm}}{\text{B}}$

Answer 1

Answer: (A)

$\overrightarrow{F}=0\Rightarrow {\overrightarrow{F}}_{\text{e}}{\overrightarrow{F}}_{\text{m}}=0\Rightarrow F_{\text{e}}=F_{\text{m}}\Rightarrow \text{qE}=\text{qVB}$
$\text{V}=\frac{\text{E}}{\text{B}}\cdot \cdot \cdot \left(1\right)$
$\text{F}=\frac{\text{d}\text{p}}{\text{d}\text{t}}=\frac{\text{Nmv}}{\text{t}}\cdot \cdot \cdot \left(2\right)$
$\text{I}=\frac{\text{Ne}}{\text{t}}\Rightarrow \text{t}=\frac{\text{Ne}}{\text{I}}\cdot \cdot \cdot \left(\text{3}\right)$
From (1), (2) and (3),
$F=$ $\frac{\text{mEI}}{\text{eB}}$