A rectangular loop of wire with sides H = 21 cm and W = 53 cm carries current I

Question

A rectangular loop of wire with sides H = 21 cm and W = 53 cm carries current I2 = 0.223 A. An infinite straight wire, located a distance L = 33 cm from segment ad of the loop as shown, carries current I1 = 0.653 A in the positive y-direction.

1)What is Fad,x, the x-component of the force exerted by the infinite wire on segment ad of the loop?

2)What is Fbc,x, the x-component of the force exerted by the infinite wire on segment bc of the loop?.

3)What is Fnet,y, the y-component of the net force exerted by the infinite wire on the loop?

Explanation / Answer

1) Fad,x = mue*I1*I2*H/(2*pi*L)

= 4*pi*10^-7*0.653*0.223*0.21/(2*pi*0.33)

= 1.85*10^-8 N (towards +x axis)

2) Fbc,x = mue*I1*I2*H/(2*pi*(L+w))

= 4*pi*10^-7*0.653*0.223*0.21/(2*pi*(0.33+0.53))

= 0.71*10^-8 N (towards -x axis)

3) Fnety = 0 (since the magnetic force on upper and lower forces are equal in magnitude and opposite)

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