A particle with a mass of 2.20 times 10-16 kg and a charge of 24.0 nC starts fro

Question

A particle with a mass of 2.20 times 10-16 kg and a charge of 24.0 nC starts from rest, is accelerated through a potential difference ?V, and is fired from a small source in a region containing a uniform, constant magnetic field of magnitude 0.600 T. The particle's velocity is perpendicular to the magnetic field lines. The circular orbit of the particle as it returns to the location of the source encloses a magnetic flux of 15.0 mu Wb. Calculate the particle's speed. Calculate the potential difference through which the particle was accelerated inside the source.

Explanation / Answer

a) flux = B A

15.0E-6 = 0.6*pi*r^2

r=2.82E-3 m

but q v B = mv^2/r

so v = q B r/( m ) = 24.0E-9*0.6*2.82E-3/(2.2E-16)=1.85E5 m/s

b) conservation of energy

q V = 1/2 mv^2

V = 0.5*2.2E-16*1.85E5^2/(24.0E-9)=156.9 V

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