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Define mutual inductance and write its S.I. units

Define the term 'mutual inductance' between the two coils.

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An air-cored solenoid with length 30 cm, area of cross-section 25 cm^{2} and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10^{−3} s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius r_{1} and the other of radius r_{2} (r_{1} < r_{2}) placed coaxially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.

(b) A rectangular coil of area A, having number of turns N is rotated at 'f' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 *πf* NBA.

In an experiment, two coils c_{1} and c_{2} are placed close to each other. Find out the expression for the emf induced in the coil c_{1} due to a change in the current through the coil c_{2}.

Draw a necessary arrangement for winding of primary and secondary coils in a step-up transformer. State its underlying principle and derive the relation between the primary and secondary voltages in terms of number of primary and secondary turns. Mention the two basic assumptions used in obtaining the above relation.

A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s^{−1} in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?