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3241004551 [841]
3 years ago
12

A charged particle enters a uniform magnetic field B_vec with a velocity v_vec at right angles to the field.It moves in a circle

with period T.1. If a second particle, with the same electric charge but tentimes as massive, enters the field with the same velocity v_vec, what is its period?A. T/10B. TC. 5TD. 10T
Physics
1 answer:
Finger [1]3 years ago
8 0

Answer:

D. 10 T

Explanation:

When a particle is moving in a magnetic field, the magnetic force provides the centripetal force that keeps the particle in circular motion.

The cyclotron period (the period the particle takes to complete one orbit) can be found to be

T=\frac{2\pi m}{qB}

where

m is the mass of the particle

q is its charge

B is the magnetic field

As we see, the period is directly proportional to the mass of the particle.

In this problem, the second particle is ten times as massive as the first one:

m' = 10 m

while the speed is the same. So, the period of the second particle is

T'=\frac{2\pi m'}{qB}=\frac{2\pi (10m)}{qB}=10 \frac{2\pi m}{qB}=10 T

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Sadly, since the force is not linear over the distance, I don't think
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I think instead we'll need to integrate the force over the distance,
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                  =  integral of (-2.85 y² dy) evaluated from  0  to  2.40

                 =  (-2.85) · integral of  (y² dy)  evaluated from  0  to  2.40 .


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And the work  =  (-2.85) · the integral

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-- There are no units in the question (except for that mysterious ' j ' after the 'F',
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-- The work done by the force is negative, because the force points
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-- It doesn't matter whether the tool goes there along the line  x=y , or
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As I hinted earlier, the last time I actually studied integration was in 1972,
and I haven't really used it too much since then.  But that's my answer
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