Question

A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.600 cm.

(a) If each wire carries 7.00 A, what are the magnitude and direction of the magnetic force per unit length acting on a wire located 0.200 cm from the center of the bundle?

Answer 1

Magnetic force is given by:

F = i*L*B

magnetic force per unit length will be

F/L = i*B

Magnetic field due to a single wire is

B = u0*i/(2*pi*r)

Now when for this packed bundle, wire located at 0.200 cm from the center of bundle, total number of enclosed wires will be

N = n*pi*r^2/(pi*R^2)

N = 100*(0.200)^2/0.600^2 = 11.11

So total magneitc field will be

B = u0*N*i/(2*pi*r)

Which means net magnetic force per unit length will be

F/L = i*B = u0*N*i^2/(2*pi*r)

F/L = 4*pi*10^-7*11.11*7^2/(2*pi*0.200*10^-2)

F/L = 0.0544 N = 54.4*10^-3 N

F/L = 54.4 mN

direction from right thumb rule will be inwards.

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