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A circular coil of N-turns and of radius R is kept normal to a magnetic field given by B = B_(0) cos omegat. Deduce an expression for emf induced in this coil. State the rule which helps to detect the direction of induced current. |
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Answer» Solution :As given circular coil of N-turns and of radius R is placed in a UNIFORM magnetic field `B = B_(0) cos Omegat` acting perpendicular to the plane of the coil, hence, total magnetic flux linked with the coil will be `phi_(B) = N A B = N (PIR^(2))B_(0), cos omegat` Since the magnetic flux is continuously varying with time, hence induced emf set up in the coil will be `phi_(B) = (dphi_(B))/DT = - d/dt[Npi R^(2) B_(0) cos omegat]` `=- NpiR^(2)B_(0)d/dt[cos omegat] = piR^(2)N B_(0) OMEGA sin omegat` Obviously the induced emf is sinusoidal in nature (of the form `omega_(0) = piR^(2)NB_(0)omega`. Direction of induced current can be DETERMINED by applying Fleming.s right hand rule. For its statement, see Point Number 31 under the heading "Chapter At A Glance". |
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