Question

A conducting single-turn circular loop with a total resistance of 2.50 ohm is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by phi_B=a + bt^2 - ct^3 where a= 5.00 Wb, b = 13.5 Wb/s^-2, and c = 5.50 Wb/s^-3. Phi_B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 1.84 s?

Answer 1

induced emf = d(phi_B)/dt

= b*2*t - c*3*t^2

= 2*b*t - 3*c*t^2

when, induced emf is maximum

d^2(phi_B)/dt^2 = 0

2*b - 3*c*2*t = 0

==> t = 2*b/6*c

= 2*13.5/(6*5.5)

= 0.818 s

so, maximum induced emf = 2*b*t - 3*c*t^2

= 2*13.5*0.818 - 3*5.5*0.818^2

= 11.05 volts <<<<<------------Answer