First slide

Force on a charged particle moving in a magnetic field

Question

A proton having kinetic energy ‘K’ is moving in a circular orbit of radius ‘R’ in a uniform magnetic field. Then the radius of an $α -$ particle moving in a circular orbit with same kinetic energy in same magnetic field will be ______

Difficult

A

R
B

$\frac{R}{2}$
C

$\frac{R}{4}$
D

2R

Solution

$\begin{array}{l} F o r t h e p r o t o n, \frac{1}{2} . m {(\frac{e B}{m} . R)}^{2} = K \\ F o r t h e α - p a r t i c l e, K = \frac{1}{2} . 4 m . {(\frac{2 e . B}{4 m})}^{2} . {(R^{1})}^{2} \\ R^{1} = R \end{array}$

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