Q1 (6 points) 1. DC motors in electric cars are famous for their \"instant torque\" at the startup. Now let us explore the mechanism of the instant torque using a (hypothetical) toy car. The DC electric motor of the toy car is made of a spinning coil between two magnets. The motor is powered by two AA batteries. The magnets inside the motor form a uniform magnetic eld of 2.0 x 10'3T. The coil in the motor is equivalent to a solenoid with 100 loops, each loop with an area of 12.0cm2. The thickness of the coil is 7.0011. Ignore the internal resistance of the battery. Ignore the self-inductance mm of the coil for parts (a)-(c). a) Suppose that the normal direction of the coil is kept perpendicular to the magnetic eld. l Calculate the torque created by the current through the coil when the coil is not spinning. b) Suppose that the motor has picked up speed, and its rate of rotation has reached f = 15H 2 (15 full turns per second). Calculate the amplitude of the induced emf in the coil while the coil is rotating. Hint: the coil also acts as an electric generator. c) The induced emf has a polarity against the emf of the batteries. Explain why the torque of an electric motor will be smaller when the rotation rate is faster. d) Calculate the inductance of the coil and discuss how the existence of inductance affects your answer to part (a). Can the motor indeed start with its maximum torque