We all know that when an electrical conductor is introduced into a magnetic field, due to its dynamic interaction with the magnetic field, emf is induced in it. This emf is known as induced emf. In this article, we will learn about motional emf where emf is induced in a moving electric conductor in the presence of a magnetic field.
Proof of motional emf:
ΦB = Blx
Where, RQ = x and RS = l,
Since the conductor is moving, x is changing with time. Thus, the rate of change of flux ΦB will induce an emf, which is given by:
Where, speed of conductor (PQ), v = -dx/dt. This induced emf due to the motion of electric conductor in the presence of magnetic field is called motional emf. Thus, emf can be induced in two major ways:
This concept of motional emf can be explained with the help of concept of Lorentz force acting on free charge carriers of conductor. Let us consider any arbitrary charge q in the conductor PQ. As the rod moves with a constant speed v, the charge is also moving with a speed v in the presence of magnetic field B. The Lorentz force on this charge is given by:
F= qvB
The work done in moving the charge from P to Q can be given by,
W = QBvl
Since, emf is defined as the work doneper unit charge,
∈ = wq = Bvl