An infinite straight wire carries a current I that varies with time as shown abo

Question

An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 3.0 A at t = t1 = 13.0 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -3.0 A at t = t4 = 28.0 s, passing through zero at t = t3 = 23.0 s. A conducting loop with sides W = 28.0 cm and L = 54.0 cm is fixed in the x-y plane at a distance d = 45.0 cm from the wire as shown.

An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 3.0 A at t = t1 = 13.0 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -3.0 A at t = t4 = 28.0 s, passing through zero at t = t3 = 23.0 s. A conducting loop with sides W = 28.0 cm and L = 54.0 cm is fixed in the x-y plane at a distance d = 45.0 cm from the wire as shown. What is the magnitude of the magnetic flux ? through the loop at time t = t1= 13.0 s? What is ?1, the induced emf in the loop at time t = 6.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise. What is ?2, the induced emf in the loop at time t = 15.0 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise. What is ?4, the induced emf in the loop at time t = 25.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise

Explanation / Answer

1) ? = 1.32e-7 Wb ---------------------------------------------------------------- 2) ? = d? = dt = 4.4154e-8 (di/dt) = 4.4154e-8 * (3/13) = -1.02e-8 V
---------------------------------------------------------------- 3) ? = 0 V ---------------------------------------------------------------- 5) ? = d? = dt = 4.4154e-8 (di/dt) = 4.4154e-8 * (3/5) = +2.65e-8 V 1) ? = 1.32e-7 Wb ---------------------------------------------------------------- 2) ? = d? = dt = 4.4154e-8 (di/dt) = 4.4154e-8 * (3/13) = -1.02e-8 V
---------------------------------------------------------------- 3) ? = 0 V ---------------------------------------------------------------- 5) ? = d? = dt = 4.4154e-8 (di/dt) = 4.4154e-8 * (3/5) = +2.65e-8 V

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