A proton is moving in a uniform magnetic field B in a circular path of radius a in a direetion perpendicular to z -axis along which field B exists. Calculate the angular momentum, if the radius is a 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 direetion perpendicular to z -axis along which field B exists. Calculate the angular momentum, if the radius is a charge on proton is e. (A)  (Be/a2) (B) eB2a  (C) a2eB (D) aeB

Tardigrade Admin · Accepted Answer

Magnetic force provides: the necessary centripetal force to the proton to move on circular path.
Under uniform magnetic field, force

e v B

acts on proton and provides the necessary centripetal force

m v^{2} / a

∴ \frac{m v ^{2}}{a} = e v B

or

v = \frac{a e B}{m} ... (i)

Now, angular momentum

J = r \times p

Here,

J = a \times m v

Putting value of

v

from Eq. (i), we get

J = a \times m (\frac{a e B}{m})

= a^{2} e B

Q. A proton is moving in a uniform magnetic field $B$ in a circular path of radius $a$ in a direetion perpendicular to $z$ -axis along which field $B$ exists. Calculate the angular momentum, if the radius is a charge on proton is $e$ .

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

$e B^{2} a$

$a^{2} e B$

$a e B$

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

a2Be​

eB2a

a2eB

aeB

Q. A proton is moving in a uniform magnetic field $B$ in a circular path of radius $a$ in a direetion perpendicular to $z$ -axis along which field $B$ exists. Calculate the angular momentum, if the radius is a charge on proton is $e$ .

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

$e B^{2} a$

$a^{2} e B$

$a e B$