9) Two long parallel wires carry currents of 4 A and 8 A in the opposite directi

Question

9) Two long parallel wires carry currents of 4 A and 8 A in the opposite direction. The wires are separated by 0.26 m.

a) Find the magnetic force per unit length between the two wires.

b) Find the magnetic field midway between the wires

c) Find the magnetic force on each wire.

The wires are then suspended horizontally one above the other with the currents flowing in same direction.

d) If the upper wire is held securely without sagging, for what mass/length will the lower wire be suspended without sagging. (Hint: there are two forces on lower wire that are exactly balanced)

Explanation / Answer

9)

F/l = uo*i1*i2/2*pi*r

part a) F/l = (4*3.14e-7*4*8)/(2*3.14*0.26) = 246e-5 N/m <----answer

part b) d = r/2 = 0.26/2 = 0.13 m

B = B1 + B2 = uo*i1/(2*pi*d) + uo*i2/(2*pi*d)

B = (uo/2*pi*d)*(i1+i2)

B = (4*3.14*12)/(2*3.14*0.13) = 184.62 T   <------------answer

+++++++++++

part c)

here to solve part c , L = length of the wire is not given

F = uo*i1*i2*L/(2*pi*r) <------------answer

part d)

Fb = m*g

uo*i1*i2*l/(2*pi*r) = m*g

uo*i1*i2*/(2*pi*r) = m/l*g

m/l = g*uo*i1*i2*/(2*pi*r)

m/l = (9.8*4*3.14e-7*4*8)/(2*3.14*0.26) = 2.412*10^-4 kg /m   <------------answer

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