A conducting circular loop has N=IO turns, radius of 25.0 cm, and resistance of

Question

A conducting circular loop has N=IO turns, radius of 25.0 cm, and resistance of 0.1 ohm it is placed in a region of an external magnetic field, so that the magnetic field lines are the field is 40 degrees relative to the surface of the loop. The strength of Calculate magnetic flux through this loop. the field starts decreasing at the rate of 0.02 T/s, determine magnitude and direction of the induced current (assume that the loop behaves like an Ohmic resistor). If, instead, magnetic field steadily increases to 1.5 T in 3 seconds, determine the induced EMF. If the change in the magnetic field strength ceases, what is the induced EMF then? Start with a good sketch, labeling relevant quantities!

Explanation / Answer

given data

N = 10 turns

r = 25 cm = 0.25 m

R = 0.1 ohms

theta = 40 degrees

B = 1.2 T

1) magnetic flux through the loop = N*A*B*cos(90-40)

= 10*pi*0.25^2*1.2*cos(50)

= 1.51 T.m^2

2) induced emf = N*A*(dB/dt)*cos(50)

= 10*pi*0.25^2*0.02*cos(50)

= 0.025 volts

3) N*A*(dB/dt)*cos(50)

= 10*pi*0.25^2*((1.5-1.2)/3)*cos(50)

= 0.126 volts

4) induced emf = 0 (when dB/dt = 0)

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