Electrons are circulating in a cyclotron in a uniform magnetic field of 1.1 T.One can think of these circulating electrons as a circular current loop with the same diameter.The magnetic field is then rapidly increased at a constant rate of 2.5 T/s.If the magnitude of the induced electric field causing the electrons to increase their speed 25 ms after the magnetic field begins increasing is 0.73 V/m,what is the diameter of the electrons' orbit? This is the basis for accelerating electrons in a betatron.
A)1.17 m
B)0.29 m
C)1.03 m
D)0.58 m
E)1.45 m

Question

Quizplus · Accepted Answer

The induced electric field is given by:$$E = \frac{dB}{dt} \cdot r$$where:* E is the electric field in V/m* dB/dt is the rate of change of the magnetic field in T/s* r is the radius of the orbit in mWe are given that:* dB/dt = 2.5 T/s* E = 0.73 V/m* t = 25 ms = 0.025 sSolving for r, we get:$$r = \frac{E}{dB/dt} = \frac{0.73 V/m}{2.5 T/s} = 0.29 m$$Therefore, the diameter of the electrons' orbit is 2 * 0.29 m = 0.58 m.

Electrons Are Circulating in a Cyclotron in a Uniform Magnetic