Depict the magnetic field lines due to two straight, long, parallel conductors carrying currents I1 and I2 in the same direction. Hence deduce an expression for the force acting per unit length on one conductor due to the other. Is this force attractive or repulsive? A rectangular current-carrying loop is placed 2cm away from a long straight current-carrying conductor. What is the direction and magnitude of the net force acting on the loop?
Answer:ℓF=2πdμ0I1I2, attractive for parallel currents; the loop is pulled towards the wire.
Solution
Parallel currents in the same direction have field lines that crowd between the wires and cancel there, drawing the wires together. Wire 1's field at wire 2 is B1=2πdμ0I1, so the force per unit length on wire 2 is
ℓF=B1I2=2πdμ0I1I2,
attractive for currents in the same direction. For the rectangular loop, only the two sides parallel to the wire give a net force; the nearer side is attracted more strongly (field ∝1/r), so the loop experiences a net force directed towards the straight conductor, of magnitude 2πμ0I1I2ℓ(d11−d21).
CBSE Class 12 Board · 2005 · All India · Subjective