A circular coil enclosing an area of 160 cm 2 is made of 190 turns of copper wir

Question

A circular coil enclosing an area of 160 cm2 is made of 190 turns of copper wire (represented by five turns in the drawing below). The wire making up the coil has negligible resistance compared to a 7.00-%u03A9 resistor which is connected across the coil to form a closed circuit. Initially, a 1.60-T uniform magnetic field towards the top of the page and perpendicularly through the plane of the coil.

(a) Assume that the direction of the field reverses at a uniform rate (so that the final magnetic field has a magnitude of 1.60 T and points through the coil and towards the bottom of the page). If the time interval required for the field to reverse directions (at this assumed uniform rate) is 0.200 s, what is the induced EMF and the induced current in this circuit during that time?

EMF:
V this is right

current:
A this is right

(b) Instead of the case described in part (a), assume that the magnetic field reverses sinusoidally during the same interval of time. In other words, the described reversal is one-half cycle of a sinusoidally-changing magnetic field with a period of 0.400 s (with the cycle beginning when the value of the field strength is a maximum). In this second case, what is the maximum induced EMF and the maximum induced current in this circuit during the 0.200-second time interval?
max EMF:
V I need help with this

max current:
A I need help with this

Explanation / Answer

T = 0.4 s
f = 1/T = 1/0.4 = 2.5

w = 2*pi*f = 15.7 rad/s

Bo = 1.6 T
A = 160*10^-4 m^2
N = 190
B = Bo*cos(w*t)

induced emf = N*A*dB/dt = N*A*Bo*sin(w*t)*w

emf = N*A*w*Bo*sin(w*t)

maximum emf = N*A*w*Bo = 190*160*10^-4*15.7*1.6 = 76.37 volts

imax = emf/R = 10.9 A

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