Superconducting cables conduct current with no resistance. Consequently, it is p

Question

Superconducting cables conduct current with no resistance. Consequently, it is possible to pass huge currents through the cables, which, in turn, can produce very large forces. Two straight, parallel superconducting cables 4.5 mm apart (between centers) carry equal currents of 15000 A in opposite directions. Find the magnitude and direction of the force per unit length exerted by one conductor on the other. Should we be concerned about the mechanical strength of these wires?

SOLUTION

SET UP (Figure 1) shows our sketch. The two currents have opposite directions, so, the forces are repulsive.

SOLVE To find the force per unit length, we use

Fl==0II2r=(4×107N/A2)(15000A)22(4.5×103m)1.0×104N/m

Therefore, the force exerted on a 1.0  m length of the conductor is 1.0×104N.

REFLECT This is a large force, somewhat greater than 1 ton per meter, so the mechanical strength of the conductors and insulating materials is certainly a significant concern. Currents and separations of this magnitude are used in superconducting electromagnets in particle accelerators, and mechanical stress analysis is a crucial part of the design process.

Part A - Practice Problem:

What is the maximum current in the conductors if the force per unit length is not to exceed 2.8×104 N/m ?

Express your answer to two significant figures and include appropriate units.

Explanation / Answer

F/l = u0*I1*I2 / 2pi*r

=> 2.8*10^4 = ((4pi*10^-7)*Imax^2) / (2pi*(4.5*10^-3))

=> Imax = 25100 A

If rounding off to 2 significant figures, then use Imax = 25000 A

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