Question

A proton is moving in a uniform magnetic field B in a circular path of radius a in a direction perpendicular to Z axis along which field B exists. Calculate the angular momentum, if the radius is a and charge on proton is e.

• A. $\frac{Be}{a^2}$
• B. $e{B}^{2}a$
• C. $a^{2}eB$
• D. $aeB$

Answer 1

Answer: (C)

Under uniform magnetic field, force evB acts on proton and provides the necessary centripetal force
$m{v}^2/a$ $\frac{m{v}^2}{a}=evB$
$v=\frac{aeB}{m}$
Now, angular momentum
$J=r\times p$ $=a\times mv$
$J=a\times m\left(\frac{aeB}{m}\right)$
$J=a^{2}eB$