Electrons are circulating in a 0.58 m diameter cyclotron orbit 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.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 rate at which the field is increasing? This is the basis for accelerating electrons in a betatron.
A)2.5 T/s
B)5.0 T/s
C)1.3 T/s
D)4.1 T/s
E)3.3 T/s

Question

Quizplus · Accepted Answer

The induced electric field (E) in a loop is related to the rate of change of magnetic flux (dΦ/dt) through Faraday's law: E = (1/2πr) * (dΦ/dt), where r is the radius of the loop. The magnetic flux Φ = B * A, where A is the area of the loop. For a circular loop, A = πr². Thus, dΦ/dt = πr² * (dB/dt). Substituting and solving for dB/dt gives dB/dt = (2E)/(r). With E = 0.73 V/m and r = 0.29 m (half of 0.58 m), dB/dt = (2*0.73)/(0.29) = 5.0 T/s.

Electrons Are Circulating in a 0