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A flat coil consists of N turns of wire and has area A. The coil is placed so that its plane is at an angle theta to a uniform magnetic field of flux density B. Obtain an expression for magnetic flux linked with the coil. The magnetic flux density B in the coil is now made to vary with time t as shown in Fig. Sketch the variation with time t of the e.m.f. induced in the coil. |
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Answer» Solution :(a) As is clear from Fig. component of magnetic FIELD along the normal to the plane of the coil is `B_("normal") = B cos (90^(@) - theta) = B sin theta`  Magnetic flux linked with the coil `phi = NB_(normal) xx A = N (B sin theta) xx A` `= N BA sin theta` (b) From t = 0 to t = T, magnetic flux density B is constant. Induced e.m.f. `e = (d phi)/(DT) =` Zero: during this interval, as shown in fig.  Between t = T and t = 2T, magnetic flux density increases from a certain value to some maximum value, Therefore, induced e.m.f. increases from zero to certain value in negative direction and becomes zero as shown in Fig. Between t = 2T and t = 3T, magnetic flux density decreases from maximum value to zero. Therefore, induced e.m.f. increases from zero to certain value in positive direction and then again becomes zero at t = 3T. The variation of induced e.m.f. with time is as shown Fig. |
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