A betatron is a charged particle accelerator that works by generating an induced

Question

A betatron is a charged particle accelerator that works by generating an induced electric field to accelerate the charged particles. In this example, it consists of a uniform magnetic field in a cylindrical region of space, generated for example by solenoidal currents. The magnetic field is varied sinusoidally. Suppose the maximum amplitude of the magnetic field over the sinusoidal variation is 0.98 T, and the frequency of oscillation is 60 Hz. What is the amplitude of the oscillating electric field at a distance 0.62 m from the axis of the betatron?

Explanation / Answer

GIven Data:

Frequency F= 60Hz

Maximum Flux Density Bmax = 0.98 T

Flux density B= Bmax*sin(2*pi*F*t)=0.98*sin(377*t) Tesla

According to the amperes circuital law

B=Mu*I/(2*pi*R) -------------------->(1)

from the above equation

I=B*2*pi*R/(Mu) ----------------------> (2)

substituing the above data in the equation 2

I=3038sin9377*t) Amps

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