Question

Two very long wires run in the z direction, one at (1,0) cm, the other at (-1,0) cm. (a) If both wires are carrying a positive current of 0.6 A upwards in z, calculate the force each wire exerts on the other. Is it repulsive or attractive? (b) Do the same problem, but with the wire at (-1,0) cm carrying 0.6 A downwards. Hint: you shouldn’t have to do any more math for this part

Answer 1

two long wire carrying currents of 0.6 A in the upward direction

and separated by a distance r = 2 cm

we know that the current carrying conductor can create a magnetic field whose magnitude is given by

B = mue0*i/2pi*r ( From Amppere's law )

and the magnetic field directions of the two wires are out of the page

the force each wire exerts on the other is F = i*l*B sin theta

sin theta = 1 , theta = 90 degrees

F/l = mue0*i1*i2/2pi*r

F/l = 4pi*10^-7*0.6*0.6/(2pi*0.02) N/m

F/l = 3.6*10^-6 N/m

from Flemings Left hand rule the direction of force by the left wire is to the right side and of the right wire to the left side means the force is attractive force

the force is attractive force

b ) if the wire at (-1,0 ) cm ( left side) current is downward then  

the magnetic force is to the left and about the right side wire is to the left so that there is a repulsive force ( From Fleming's left hand rule)

the magnetic force magnetude is same 3.6*10^-6 N/m exerts one on the other