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Dynamic (Motional) Emi due to Translatory Motion

Consider a conducting rod of length l moving with a uniform velocity 88590.png perpendicular to a uniform magnetic field 88580.png, directed into the plane of the paper. Let the rod be moving to the right as shown in Fig. 5. The conducting electrons also move to the right as they are trapped within the rod.
Fig. 5
Conducting electrons experience a magnetic force Fm = evB. So they move from P to Q within the rod. The end P of the rod becomes positively charged while end Q becomes negatively charged. Hence an electric field is set up within the rod which opposes the further downward movement of electrons, i.e., an equilibrium is reached and in equilibrium Fe = Fm, i.e., eE = evB or E = vB Induced emf e = El = Bvl [E = V/l]
If rod is moving by making an angle θ with the direction of magnetic field or length, Induced emf, e = Bvl sinθ.
Fig. 6

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