Question #0ad8d

1 Answer
Mar 23, 2017


Two electric current carrying units would exert a magnetic force on one another.


We know that an electric current produces a magnetic field in its surroundings.

The magnitude of the magnetic field may be given using Biot-Savart law or Ampere's law.

From Lorentz force law, one finds that a magnetic field is capable of exerting a force on a moving charged particle.

So consider two wires in each other's vicinity, both carrying a certain current and hence producing magnetic fields of their own.
Now, electric currents are constituted by the flow of electric charges. So, the magnetic field produced by wire 1 interacts with the moving charges inside the wire 2 and exert a Lorentz force.

That is what precisely happens.

By Newton's third law, the field of wire 2 inturn exerts a similar force in opposite direction on the charges moving inside wire 1.

Quantitatively analysing the simplest case where two parallel long wires carry currents #I_1# and #I_2#.

Using Biot-Savart law or by Ampere's law that the magnetic field by first wire at the location of the second is,

#vec B_1 = mu_0/(2pi)*I_1/a# pointing in the circumferential direction where #a# distance between the two parallel wires.

Also, by Lorentz force law, one obtains that for wire 2 carrying current #I_2# of length #l# in Magnetic field #B_1#, it experiences a net Lorentz force,

#vecF = I_2 (vecl X vecB_1)#

Since in this case the magnetic field is in circumferential direction and the direction of current perpendicular to it, the magnitude of force is,

#F =I_2*l*B_1#

Thus force per unit length of the second wire would be,

#f = I_2*B_1#

#implies f = mu_0/(2pi)*(I_1I_2)/a #