Question

B2 If a rectangular coil, with length ofa and height of V3a ( = 1m), is rotating at an angular velocity, o -50 rad/s, in a B-field. At the starting position, the plane of the coil is exactly normal to the B-field as shown in Fig. B2a (1) What is the induced e.m.f. in the coil? (in V) (4 marks) (2) What is the induced e.m.f. if the starting position is paralleled to the B-field as (4 marks) shown in Fig. B2b? (in V) (3) If the coil in part (1) is replaced by a hexagon one with same dimension as shown in Fig. B2c, what is the induced e.m.f. in the coil? (in V) (4 marks) (4) If the resistance of the coil is 5(2 / m, what is torque of the rectangular coil when it passes through the position shown in part (2)? (Hint: determine the current direction first). (N.m) (3 marks) X X X X X X em.f X X X X X X B=-10, T 0 0 Fig. B2a Fig. B2b X X e.m.f Fig. B2c

Answer 1

For a coil rotation in a magnetic field B, induced emf can be found as E = B A n w sin (theta) B. Mag. field A: Area of the coil n: No of terms w Angular velocity E = contourintegral_L (u times B). dl E = -d phi/dt = - d/dt [B times A cos theta] = n (B times A) w sin theta = Here n = 1 B = -10 a^^_x A = squareroot 3 a^2 w = 50 rad s^-1 E = 1 (-10 a^^_x times (squareroot 3 a^2) a^^_x) 50 sin = -10 squareroot 3 a^2 (a^^_x times a^^_x) so sin theta \r\n E = -500 squareroot 3 a^2 sin theta Here Area is paralleled. So normal becomes is (which represent the area direction of the object) E = n (B times A) w sin theta = n (-10 a^^_x times squareroot 3 a^alpha a^^_z) so sin theta = -500 squareroot 3 a^2 (a^^_x
E= BAnw sin