Two circular loops are centered on the x-axis parallel to the yz-plane. The smal

Question

Two circular loops are centered on the x-axis parallel to the yz-plane. The smaller loop is stationary with radius r = 0.014 m, and resistance R = 0.003 Ohms. The larger loop has radius, s = 0.14 m, carries current I = 1.5 A, and moves towards the smaller loop with speed v = 200 m/s. Find the current induced in the smaller loop when the larger loop is x = 0.9 m away. What is the direction of current through the smaller loop compared to the direction of current in the larger loop? Is it in the same or the opposite direction?

Explanation / Answer

smaller loop magnetic field:

B = (ÃŽ ¼i/2) * (r^2/(r^2+x^2)3/2)

dB/dx = (ÃŽ ¼i/2) * ((-r^2)(3/2)(r^2+x^2)1/2(2x)/(r^2+x^2)3)

         = (ÃŽ ¼i/2) * ((-r^2)(3/2)(2x)/(r2+x2)5/2)

         = (4*3.14e-7*1.5/2)*(0.014*0.014*(3/2)*(2*.9)/(0.014*0.014+.9*.9)^(5/2))Â

         = 8.437*10^-10 T/m

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ÃŽ µ = dÆ/dt

  = A dB/dt

  = Às2 (dB/dx)(dx/dt)

  = Às2 (dB/dx)(v)

  = 3.14*0.14*0.14 * (8.437*10^-10) * (200)

  = 1.03*10^-8 V

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i = ÃŽ µ/R = 1.03*10^-8/0.003 = 3.46 * 10^-6Â A

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