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  4. A proton of mass ‘m’ moving with a speed v (<< c, velocity of light in vacuum) completes a circular orbit in time ‘T’ in a uniform magnetic field. If the speed of the proton is increased to 2 v, what will be time needed to complete the circular orbit ?

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Q. A proton of mass ‘$m$’ moving with a speed $v (<< c$, velocity of light in vacuum) completes a circular orbit in time ‘$T$’ in a uniform magnetic field. If the speed of the proton is increased to $2\, v$, what will be time needed to complete the circular orbit ?

WBJEEWBJEE 2018Moving Charges and Magnetism

Solution:

$\because$ When a charged particle moves at a circular path in uniform magnetic field, it time period is independent from its speed.
$\therefore $ Time period of proton will not change with change in its speed