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T is directly proportional to the mass 'm' and inversely proportional to magnetic field 'B'
Explanation:
for a charge moving with a velocity 'v' perpendicular to a magnetic field 'B',
the charge experiences LORENTZ FORCE.
This Lorentz force produces necessary centripetal force.
Lorentz force = q v B
Centripetal force = m / R R ⇒ radius of circular path
so then ,
q v B = m / R
R = m v / q B ----------------------- ( 1 )
we know that ,
T = (distance ) / (velocity)
T = 2 π R / v
from ( 1 ),
T = ( 2 π m ) / ( q B )
hence the time period is directly proportional to the mass 'm' and inversely proportional to the magnetic field 'B'
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