at the i th area element. d A i represents area vector of the i th area element. * Note that sensitive electrical instruments in the vicinity of an electromagnet can be damaged due to the induced emfs (and the resulting currents) when the electromagnet is turned on or off. E XAMPLE .
The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit. Mathematically, the induced emf is given by – d B Φ ε = ( . ) The negative sign indicates the direction of ε and hence the direction of current in a closed loop. This will be discussed in detail in the next section.
In the case of a closely wound coil of N turns, change of flux associated with each turn, is the same. Therefore, the expression for the total induced emf is given by – B N Φ ε = ( . ) The induced emf can be increased by increasing the number of turns N of a closed coil. From Eqs.
( . ) and ( . ), we see that the flux can be varied by changing any one or more of the terms B , A and θ . In Experiments .
and . in Section . , the flux is changed by varying B . The flux can also be altered by changing the shape of a coil (that is, by shrinking it or stretching it) in a magnetic field, or rotating a coil in a magnetic field such that the angle θ between B and A changes.
In these cases too, an emf is induced in the respective coils. Example . Consider Experiment . .
(a) What would you do to obtain a large deflection of the galvanometer? (b) How would you demonstrate the presence of an induced current in the absence of a galvanometer? Solution (a) To obtain a large deflection, one or more of the following steps can be taken: (i) Use a rod made of soft iron inside the coil C , (ii) Connect the coil to a powerful battery, and (iii)