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?

What is the maximum current in the conductors if the force per unit length is not to exceed 4.3×104 N/m ?

Explanation / Answer

magnetic field produced by each wire at the location of other

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

magnetic force Fb = i*L*B

magnetic force per unit length = Fb/L

magnetic force per unit length = uo*i*i/(2*pi*r)

magnetic force per unit length = 4*pi*10^-7*15000*15000/(2*pi*4.5*10^-3) = 10000 N

------------------------

if magnetic force per unit length = 4.3*10^4 N

4.3*10^4 = 4*pi*10^-7*Imax^2/(2*pi*4.5*10^-3)

Imax = 31104.6 A

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