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=0.01m, and resistance R=0.003Ohms. The larger loop has radius, s=0.1m, carries current I=1.5A, and moves towards the smaller loop with speed v=220m/s.
Find the current induced in the smaller loop when the larger loop is x=1.2m away. What is its direction?
Iinduced =___A
Compared to the direction of current through the larger loop, the current through the smaller loop moves in (Choose One):

__the same direction.
__the opposite direction.

Explanation / Answer

B = (i/2)*(R2/(R2+x2)3/2)

R = s = 0.1 m

dB/dt = (dB/dx) * (dx/dt)

          = (dB/dx) * (v)

          = (iR2/2)*((-3/2)*(2x)*((R2+x2)-5/2)) * (220)

         = (4*3.14e-7*1.5*0.12/2)*(-3)*1.2*(0.12+1.22)-5/2)*(220)

         = -2.9469e-6 T/s

------------------------------------------------

= -d/dt

= -A*(dB/dt)

= (3.14*0.01*0.01) * (2.9469e-6)

= 9.2533 * 10^-10 V

------------------------------------------------

i = V/R = 9.2533e-10/0.003 = 3.08 * 10^-7 A

-------------------------------------------------------------

the opposite direction.

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