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A metallic rod of length l is moved perpendicular to its length with velocity v in a magnetic field vecB acting perpendicular to the plane in which rod moves. Derive the expression for the induced emf. Or Starting from the expression for the Lorentz force acting on the free charge carriers of a conductor moving in a perpef Zicular magnetic field, obtain the expression for the motional emf induced. |
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Answer» Solution :Let a conducting ROD PQ of length L is moved in a uniform magnetic field `vecB` with a velocity `vecv` such that `vecB` acts perpendicular to the plane of motion of rod PQ, consider any free charge in the conductor PQ. As the rod moves, the charge q ALSO moves with same velocity and experiences a Lorentz force of magnitude F = q uB and its direction is from Q to P. All free charges experiences the same force IRRESPECTIVE of their positions in the rod PQ. `therefore` Work done in MOVING the charge from Q to P is W = Fl = q v B l Since emf is the work done per unit charge, hence emf induced in the rod will be given by `|varepsilon| = W/q = (q vBl)/q = Blv` 
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