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. $\frac{m E I}{e B}$
• B. $\frac{m I E}{e}$
• C. $\frac{m E I}{B}$
• D. $\frac{e I m}{B}$

Answer 1

Answer: (A)

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