A loop wire (resistance of 2.0 mOhms) is positioned with respect to a long wire

Question

A loop wire (resistance of 2.0 mOhms) is positioned with respect to a long wire which carries current . If d is 1.0 cm D is 6.0 cm and L is 1.5 m, wgat current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s? A loop wire (resistance of 2.0 mOhms) is positioned with respect to a long wire which carries current . If d is 1.0 cm D is 6.0 cm and L is 1.5 m, wgat current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s?

Explanation / Answer

According to the given problem,

Faraday's Law says the emf induced in a loop of area A = d(BA)/dt where BA is the magnetic flux thru the loop

A = 1.5m*0.06m = 0.09m²

We know B=µo*I/2r =4*10-7*I/(2*3.5*10-2)
B = (4/7)*10-5 * I
d(BA)/dt = 9e-2 * (4/7)e-5 * dI/dt
d(BA)/dt = 36/7 *10-5 = the emf induced around the loop.

Now divide that by the resistance = 2*10-3

36/14 * 10-2 = 25.7mA or about 26mA <-----
The closest to that is answer C = 27mA

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