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Derive the expression for emf induced in a straight conductor moving perpendicular to a uniform magnetic field. |
Answer» Solution :Let .PQ. represent a conductor moving with a speed `nu` at right angles to the magnetic flux density .B. pointing PERPENDICULAR to the sheet of paper and pointing towards the paper. Let RQ= x be the DISTANCE coverered by the conductor. Magnetic flux `Phi_B =Blx`.  INDUCED emf `=-(d(Phi_E))/(dt)=-d/(dt)(Blx)` i.e., `e=-Bl(dx)/(dt)` But,`(-dx)/(dt)=nu` `thereforee=Blnu""` ...........(1) Note : The Lorentz force acts on a change in a conductor and acts along PQ. done in moving a charge .q. from P to Q is W= (Lorentz force ) (displacement of the charge .q.) i.e.,W =`(Bqnu)L` by DEFINITION electric p.d`=W/q=(Bqnul)/q=Bnul`...............(2) Equation (1) and (2) are identical. |
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