a) For a circular coil of 10 turns, radius 0.1 m and a total resistance of 1.0 O

Question

a) For a circular coil of 10 turns, radius 0.1 m and a total resistance of 1.0 Ohm, how much current is induced if a magnetic field changes at a rate of 0.5 T/s through it? Assume that the effective area of a maximum and the coil is stationary. Units mA

b) Consider a square loop of wire (sides of 0.25 m) with a resistor included. A bar magnet with the north end up front is approaching the closed loop and thus induces a current. If the resistor has a resistance of 1.5 Ohms, and the rate of change of magnetic field due to the incoming bar magnet is 0.01 T/s, what is the rate of energy dissipation across the resistor?

Explanation / Answer

The induced voltage can be found by: E = N(BA)/t E = 10(0.5)(pi)(.1^2) E = .157 V The induced current can be found using Ohm's Law: V = IR E = IR .157 = I(1) I = .157 A I = 157 mA (b) The induced voltage can be found by: E = N(BA)/t E = 1(.01)(.25^2) E = 6.25e-4 V The induced current can be found by: E = IR 6.25e-4 = I(1.5) I = 4.2e-4 A the rate of energy dissipation is the power dissipated across the resistor: P = (I^2R) P = (4.2e-4)^2(1.5) P = 2.6e-7 W BOL

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