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.

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)  (Be/a2)  (B)  eB2a  (C)  a2eB  (D)  aeB

Tardigrade Admin · Accepted Answer

Under uniform magnetic field, force evB acts on proton and provides the necessary centripetal force (mv2/a) (mv2/a)=evB v=(aeB/m) Now, angular momentum J=r× p =a× mv J=a× m( (aeB/m) ) J=a2eB

Q. 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 $e$ .

$\frac{B e}{a ^{2}}$

$e B^{2} a$

$a^{2} e B$

$a e B$

Under uniform magnetic field, force $e v B$
acts on proton and provides the necessary centripetal force
$\frac{m v ^{2}}{a}$
$\frac{m v ^{2}}{a} = e v B$
$v = \frac{a e B}{m}$
Now, angular momentum
$J = r \times p$
$= a \times m v$
$J = a \times m (\frac{a e B}{m})$
$J = a^{2} e B$

Q. 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.

a2Be​

eB2a

a2eB

aeB