A packed bundle of 150 long, straight, insulated wires forms a cylinder of radiu

Question

A packed bundle of 150 long, straight, insulated wires forms a cylinder of radius R = 0.560 cm. If each wire carries 2.05 A, (a) What is the magnitude of the magnetic force per unit length acting on a wire located 0.210 cm from the center of the bundle? 4.73E-5 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N/m (b) What is the direction of the magnetic force per unit length acting on a wire located 0.210 cm from the center of the bundlei? toward the center of the cylinder O away from the center of the cylinder parallel to the wires c) Would a wire on the outer edge of the bundle experience a force greater or smaller than the value calculated in parts (a) and (b)? O greater O smaller Give a qualitative argument for your answer.

Explanation / Answer

from Ampere's law

B*2*pi*r = uo*I_enclosed

B = magnetic field at a distance r from cylinder

n = number of bundles

I_enclosed = current density *pi*r^2

r = 0.21 cm = 0.0021 m

current density = n*I/(pi*R^2)

R = 0.56 cm = 0.0056 m

B*2*pi*0.0021 = 150*4*pi*10^-7*2.05/(pi*0.0056^2)*(pi*0.0021^2)

B = 4.12E-3 T

magnitude of magnetic force Fb = I*B = 2.05*4.12E-3

Fb = 8.45E-3 N/m

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toward the center of cylinder

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greater

r = R

B = uo*I*n/(2*pi*R)

Fb = B*I

Fb = uo*I^2*n/(2*pi*R)

Fb = 4*pi*10^-7*2.05^2*150/(2*pi*0.0056)

Fb = 22.5E-3 N

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