Two long parallel current carrying conductors are 0.4m apart in air and carrying currents 5A and 10A respectively.Calculate the force per metre on each wire,if the currents are in the same direction and in the opposite direction.(meu knot=4π×10 raise to -7 Wb/Am)

Kapil Khare
80 Points
4 years ago
Let us first consider 2 long parallel wires separated by distance d. Wire1 carries current I1 and Wire2 carries I2.
Wire2  will experience magnetic field due to current in Wire1
B1 = ($\mu$I1/2$\pi$d)
perpendicular to the plane containing both the wires.
Thus the force per unit length
$\lambda$ = force/length = ($\mu$I1I2/2$\pi$d)
We consider both wire to be very long and then according to newton’s third law of motion
Force per unit length experience by Wire2 is equal to Force per unit length experienced by Wire1, that means, both wires will experience the same force per unit length.
Now let us consider that both the wires are vertically in the plane of paper and dirction of current in both wires are upwards. Wire1 is in left side. Then direction of Magnetic field experience by Wire2 will be into the paper and thus the force experienced will be towards Wire1.
Thus when the direction of current is same the force is attractive and similarly, when the direction of current is opposite, the force is repulsive.

So, for given question if the direction of current is same
$\lambda$ = [(4$\pi$*10-7)*5*10/(2$\pi$*0.4)]
$\lambda$ = 2.5*10-5N/m
towards each other.
The magnitude will be same when currents are in opposite direction but direction is away from each other.