In a certain betatron, the radius of the electron orbit is 32 cm and the magnetic field at the orbit is given by , where t is in seconds and is in tesla. In the betatron, the average value of the field enclosed by the electron orbit is equal to twice the value at the electron orbit. (a) We have to calculate the induced electric field felt by the electrons at . We have to find the acceleration of the electrons at this instant. We may ignore the relativistic effects.

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In the betatron the magnetic field at the orbit is

.

and as the average value of the field enclosed by the electron orbit is equal to twice the value at the electron orbit, we have

.

As the radius of the electron orbit is 32 cm, the flux enclosed by the electron orbit will be

By applying the Faraday’s law, we find that the induced electric field at the orbit will be

The acceleration of the electrons at this instant will therefore be