A coil of 50 turns sits in a vertical magnetic field with a variable magnetic fi

Question

A coil of 50 turns sits in a vertical magnetic field with a variable magnetic field. The field varies as a sinusoidal according to the equation B = 5.00sin[(?/2)t] (where t is in seconds). Each layer of the coil is 0.005 mm and the total coil has a volume of 6.25x10-4 ? m3. If the coil has an internal resistance of 5 Ohms, determine

a) the induced voltage in the coil between the times ti = 0.33s to tf =0.67s

b) the induced current in the coil

c) Now suppose the coil oscillates back and forth. Suppose that at ti = 0.33 s the area of the coil is pointed at an angle of 30 degrees from the vertical, and at tf = 0.67 s the coil is 10 degrees from the vertical. Find both quantities from above.

Explanation / Answer

emf = rate of change in flux

emf = (d/dt)*(B*A)

emf = A*(dB/dt) = A*5*cos(pi/2)*t * (pi/2)

emf = 0.00785*5*(3.14/2)*cos(1.5s(1.57*0.33) - cos(1.57*0.67)

emf = 0.0229 v

b) i = e/R = 0.0229/5 = 0.00458 A

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