NYJC_EJC 2026 Electromagnetic Induction and AC Tutorial

9814 H3 Physics (2026) EMI & AC Tutorial 1 Electromagnetic Induction 1 Fig. 1.1 below shows a metal bar of length L moving at a constant velocity v parallel to a long, straight wire carrying a steady current I. (a) Show that the magnitude of the emf induced is 0 ln 12 v L a   =+  I (b) If the bar is replaced by a rectangular wire loop of resistance R, as shown in Fig. 1.2, what is the magnitude of the current induced in the loop? 2 An induction furnace uses electromagnetic induction to produce eddy currents in a conductor, thereby raising the conductor’s temperature. Commercial units operate at frequencies ranging from 60 Hz to about 1 MHz and deliver powers from a few watts to several megawatts. Induction heating can be used for warming a metal pan on a kitchen stove. By creating an induced current for a short time interval at an appropriately high frequency, one can heat a sample down to a controlled depth. To explore induction heating, consider a flat conducting disk of radius R, thickness b, and resistivity ρ. A sinusoidal magnetic field B0cos(ωt) is applied perpendicular to the disk. Also assume the eddy currents occur in circles concentric with the disk. (a) Calculate the average power delivered to the disk. (b) By what factor does the power change when the amplitude of the field doubles? When the frequency doubles? When the radius of the disk doubles? 3 A long, straight wire of negligible resistance is bent into a V shape, its two arms making an angle α with each other, and placed horizontally in a vertical, homogeneous magnetic field of strength B. A rod of total mass m, and resistance r per unit length, is placed on the V-shaped conductor, at a distance x0 from its vertex A, and perpendicular to the bisector of the angle α, as shown in Fig. 3.1. v a L I Fig. 1.1 I v a L Fig. 1.2 Fig. 3.1

9814 H3 Physics (2026) EMI & AC Tutorial 2 The rod is started off with an initial velocity v0 along the bisector, and away from A. The rod is long enough not to fall off the wire during the subsequent motion, and the electrical contact between the two is good – although the friction between them is negligible. T is the area of the triangle formed by the rod and the wire at that instant. (a) Derive the magnetic force acting on the rod. . State the direction of the force relative to the velocity of the rod. (b) Apply Newton’s Second Law to show that =− 2dd dd v B Tm t r t . State the meaning of the negative sign. (c) Let the distance between the rod and A at an instant in time be x. Express the area T in terms of x and α. (d) Hence, determine the distance at which the rod will stop moving in terms of m, r, B, α, v0 and x0. Alternating Current 4 (a) A transformer connected to a 50 Hz AC supply may emit a humming sound. A student relates the sound to the windings of each coil