A circuit board with a rectangular conducting path is positioned near a very lon

Question

A circuit board with a rectangular conducting path is positioned near a very long straight wire, as shown in (Figure 1) . A current of  3.1 A flows through the wire and through the conducting rectangle in the directions shown.

Part A: Find the magnitude of the net force on the circuit board if  w = 5.8 cm, d = 2.7  cm, and L= 11.4 cm.

F = _______N

Part B: What is the direction of the net force on the circuit board? (choose one)

A. towards the wire

B. away from the wire

C. in the direction of the current in the long wire

D. out of the plane of the figure

Explanation / Answer

here,

magnetic feild due to current carying wire , B = u0 *I/(2 * pi * r)

force on current carying wire , F = B*I*L * sin(theta)

w = 0.058 m

d = 0.027 m

L = 0.114 m

I = 3.1 A

part A)

the net force on the reactangle , F = (u0*I/(2*pi*(d))) *I*L - (u0*I/(2*pi*(d + w))) *I*L

F = (u0*3.1/(2*pi*(0.027))) *3.1*0.114 - (u0*3.1/(2*pi*(0.027 + 0.058))) *3.1*0.114

F = 5.55 * 10^-6 N

the net force on the rectangle is 5.55 * 10^-6 N

part B)

the direction of net electric force is away from the wire

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