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(a) Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it. (b) The current flowing through an inductor of self-inductance L is continuously increasing. Plot a graph showing the variation of (i) Magnetic flux versus the current (ii) Induced emf versus dI//dt (iii) Magnetic potential energy stored versus the current. |
Answer» Solution :(a) Prepare a coil AB of few turns of enamelled copper wire and join its ends to a sensitive galvanometer G. Take a strong bar magnet NS and quickly bring north pole N of magnet towards the coil AB. We find that galvanometer G gives a momentary deflection towards right and current induced in the coil flows in an anticlockwise direction when seen from the side of magnet. Due to the approaching magnet the magnetic flux of coil AB increases. The induced current opposes this increase in magnetic flux and as a result the end A of the coil acquires N polarity so as to oppose the motion of approaching magnet (FIG. 6.56 (a)].  If now the magnet NS is taken away from the coil AB, we again GET a momentary deflection in galvanometer G but now the induced current is flowing in clockwise direction when seen from the side of magnet NS. Thus, end A of the coil is now behaving as Spole and opposes the away motion of magnet NS. Thus, it is demonstrated that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it. (b) Here current I flowing through an inductor of self-inductance Lis continuously increasing at a constant rate. Thus, `(dI)dt = a` a constant. (i) As magnetic flux `phi_(B) = LI` and I is continuously increasing, hence `phi_(B)` is also increasing proportionately. Therefore `phi_(B) - I` graph is a straight line inclined to the axes as shown in Fig. 6.57(a). (ii) Induced emf `|epsi|= L (dI)/dt and (dI)/dt` is a constant. Therefore, MAGNITUDE of induced emf is also a constant. So `varepailon - (dI)/dt` graph is a straight line parallel to `(dI)/dt` AXIS as shown in Fig. 6.57(b). (iii) Magnetic potential energy stored in the inductor `U_(B) = 1/2LI^(2)`. Therefore, `U_(B) - I` parabolic curve as shown in Fig. 6.57(c). 
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