A charged particle with charge Q is moving with speed V in a uniform magnetic field. A second identical charged particle is moving with speed 2V perpendiculuar to the same magnetic field. The time to complete one full circular revolution for the first particle is t1 . The time to complete one full circular revolution for the particle moving with speed 2V is
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To find the time to complete one full circular revolution for the particle moving with speed 2V, we can use the formula for the period of a charged particle in a magnetic field:
T = 2πm / (qB)
Where:
T is the period or time to complete one full circular revolution,
m is the mass of the particle,
q is the charge of the particle,
B is the magnetic field strength.
Since the two particles are identical, their masses and charges are the same. The only difference is their speeds: V and 2V. Therefore, we can say that the period of the second particle is proportional to its speed.
To find the relation between the periods of the two particles, we can set up a ratio:
t1 / T2 = V / (2V)
Simplifying the expression, we get:
t1 / T2 = 1 / 2
Now we can solve for T2, the time to complete one full circular revolution for the particle moving at 2V:
T2 = t1 * (2 / 1) = 2 * t1
Therefore, the time to complete one full circular revolution for the particle moving at 2V is 2 times the time to complete one full circular revolution for the particle moving at V.