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Question

For full points/best answer you must provide me a detailed explicit solution. Please define all variables and equations. THanks

In Figure 28.17, a rectangular current loop is carrying current I1 = 3.0 A, in the direction is located near a long wire carrying a current lw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire. If the net force on the loop is to have magnitude 4.9 times 10-6 N and is to be directed towards the wire, what must be the (a) magnitude and (b) direction (from top to bottom or from bottom to top in the sketch) of the current lw in the wire? (NOTE: mu0 = 4pi times 10-7 T m/A.)

Explanation / Answer

let, l = 0.8 m

bredth, b = 0.6 m

distance between loop and wire, a = 0.1 m

I1 = 3 A

Let IW is the current in the wire

magnetic force on the left segment, FL = mue*I1*IW*l/(2*pi*a)

= 4*pi*10^-7*3*I2*0.8/(2*pi*0.1)

= Iw*4.8*10^-6 N (towards left)

magnetic force on the right segment, FR = mue*I1*Iw*l/(2*pi*(a+b))

= 4*pi*10^-7*3*Iw*0.8/(2*pi*(0.7))

= Iw*6.86*10^-7 N (towards right)

magnetic force on upper and lower segments are equal in magnitude and acts opposite direction.

so,

Fnet = FL - FR

4.9*10^-6 = Iw*4.8*10^-6 - Iw*6.86*10^-7

Iw = 4.9/(4.8 - 0.686)

= 1.19 A <<<<<<<<------------Answer

Direction : Upward <<<<<<<<------------Answer

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