Question

The magnetic force experienced by an electron moving with a velocity of $2775km{s}^{-1}$ at an angle of ${30}^{\circ }$ to a magentic field is $7.336\times {10}^{-14}N$. What is the strength of the magnetic field (in Tesla)? Given, the electron charge, $e=1.6\times {10}^{-19}C$

• A. $1.28$
• B. $0.33$
• C. $0.26$
• D. $1.09$

Answer 1

The correct option is B $0.33$

Magnetic force (F) experienced by the electron in the magnetic field B is given by:
$F=Bev$(sin$\theta$)
where velocity of the electron, $v$ = $2775km{s}^{-1}$ = $27.75\times {10}^{5}m{s}^{-1}$ and angle between velocity of the electron and magnetic field, $\theta ={30}^{\circ }$
Substituting the given values, we get
$7.336\times {10}^{-14}$ = $B\times 1.6\times {10}^{-19}$ $\times 27.75\times {10}^5\times \text{sin}\left({30}^{\circ }\right)$
On solving, $B=0.33T$.