Need parts b, d, and f please. A circular wire loop of radius r = 0.085 m and re

Question

Need parts b, d, and f please.

A circular wire loop of radius r = 0.085 m and resistance R = 11.3 Ohm rotates about a shaft through its diameter at a constant rate of f = 11.4 Hz in a uniform B = 0.48-T magnetic field directed perpendicular to the rotation axis. The plane of the loop is perpendicular to the magnetic field at time t = 0. (a) Select the correct expression for the time-dependent magnetic flux through the loop. (b) Find the value of the magnetic flux through the loop, in webers, at time t = 4.3 s. (c) Select the expression for the time-dependent emf induced in the loop based on the expression you entered in part (a) (d) Calculate the induced emf in the loop, in volts, at time t = 4.3 s. (e) Select the expression for the induced current in the loop based on the expression you entered in part (c). (f) Find the induced current in the loop, in amperes, at time t = 4.3 s.

Explanation / Answer

magnetic flux = N*B*A*coswt

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part(b)

w = 2*pi*f = 2*pi*11.4 = 71.6 rad/s

A = pi*r^2 = pi*0.085^2 = 0.0226 m^2

flux = 1*0.48*0.0226*cos(71.6*4.3)

flux = 0.01085 T m^2

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part(c)

induced emf = -rate of change in flux

emf = -(d/dt)*N*B*A*cos(wt)

emf = -N*B*A*w*sinwt

===================================

part(d)

induced emf = - 1*0.48*0.0226*71.6*sin(71.6*4.3) = 0.003045 V

========================

part(e)

from ohms law

induced current = induced emf/resistance

induced current = N*B*A*w*sinwt/R

====================

part(f)

induced current i = 0.003045/11.3 = 0.0002695 A

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