Two coplanar and concentric circular loops of wire carry currents of I 1 = 5.90

Question

Two coplanar and concentric circular loops of wire carry currents of I1 = 5.90 A and I2 = 2.80 A in opposite directions as in the figure below. Let r1 = 12.0 cm and r2 = 8.50 cm.

(a) What is the magnitude of the net magnetic field at the center of the two loops?
µT

(b) What is the direction of the net magnetic field at the center of the two loops?

out of the pageinto the page    toward the top of the pagetoward the bottom of the page

(c) Let r1 remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 such that the net field at the center of the loops is zero.
cm

Explanation / Answer

a) Bnet = B1 - B2

= mue*I1/(2*pi*r1) - mue*I2/(2*pi*r2)

= 4*pi*10^-7*5.9/0.12 - 4*pi*10^-7*2.8/(2*pi*0.085)

= 5.52*10^-5 T

= 55.2 micro T

b) into the page

c)

Bnet = B1 - B2

0 = mue*I1/(2*pi*r1) - mue*I2/(2*pi*r2)

mue*I1/(2*pi*r1) = mue*I2/(2*pi*r2)

I1/r1 = I2/r2

r2 = r1*(I2/I1)

= 12*(2.8/5.9)

= 5.69 cm

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