RI 17 Electromagnetic Induction tutorial solutions

RAFFLES INSTITUTION PHYSICS DEPARTMENT 1 Tutorial 17 Electromagnetic Induction Suggested Solutions D1 (a) (b) (c) Φ t 0 E t 0 • t2 < t1 • magnitude of peak emf is larger in the duration t 2 • Area under E-t graph is equal for the duration t1 and the duration t2 t1 t2 • t2 = t1 • magnitude of peak emf is equal in both durations • Area under E-t graph is equal for the duration t 1 and the duration t2 Φ t 0 E t 0 t1 t2 Φ t 0 E t 0

RAFFLES INSTITUTION PHYSICS DEPARTMENT 2 D2 (a) Faraday’s Law states that the induced e.m.f. E is directly proportional to the rate of change of magnetic flux linkage through the coil. Mathematically, dE dt=− Φ Therefore, E dt∆= − ∫Φ The area under the E-t graph is obtained by integrating E over a particular time duration. From the expression above, the magnitude of the area under the curve ( E dt−∫ ) gives the change in magnetic flux linkage(∆Φ) through the coil. (b) ( )( ) 33 33 Area under curve number of squares area of one square 9.5 50 10 10 10 4.75 10 Wb 4.8 10 Wb −− −− ∆= = × =×× × = × ≈× Φ (c) ( ) 3 23 0 4.75 10 0.052 T 34 10100 2 final initial NBA B NA π − − ∆= − =− ∆×∴= = =  ×  ΦΦ Φ Φ D3 (a) (b) Φ t 0 E t 0 T T t 0 (ii) E (i) Φ T 2T

RAFFLES INSTITUTION PHYSICS DEPARTMENT 3 D4 (a) (b) When a magnet approaches the coil, the magnetic flux linkage through the coil increases and an e.m.f. would be induced in the coil according to Faraday’s Law. According to Lenz’s Law, the induced e.m.f. would be negative so as to oppose the increasing flux linkage. When the magnet moves away from the coil, the magnetic flux linkage through the coil decreases. Induced e.m.f. would be positive so as to oppose the decreasing flux linkage. The magnitude of the e.m.f. is the greatest where the magnetic flux linkage changes at the greatest rate, i.e., at the points of inflection of the Φ - t graph. The induced e.m.f. is zero at the turning points of the Φ - t graph where gradient is zero. In between the magnets, the flux linkage of the coil remains zero for a certain duration of time. The induced e.m.f. is therefore zero during this period. *Note: • the actual shape/equation of the variation is not as important as recognizing the general trend of the variation • i.e. magnetic flux linkage increases to a maximum before decreasing to zero for a while before the next magnet passes through; the emf induced is in opposite directions when the magnet enters and leaves the position of the coil

RAFFLES INSTITUTION