Problem 3 12 points The speed sensor for an automotive cruis

Problem 3: 12 points The speed sensor for an automotive cruise control consists of a magnet mounted on the drive shaft along with a coil of wire mounted on the chassis. As the magnet passes the coil, an emf is induced for a short period of time. The number of induced emfs occurring per second allows a computer to determine the drive shaft speed and ultimately the speed of the car. What is the polarity of the emf when the magnet is at the three positions A, B, and C shown in the drawing? Assume the north pole of the magnet is closest to the coil.

Solution

Here ,

at position A ,

as the magnetic field due to magnet is to the right and it is increasing at the location of the coil ,

hence , the magnetic field due to coil is to the left

the current will flow from 2 to 1 , hence , 2 is positive

at position B

as the magnetic flux due to bar magnet will be constant

there is emf in the solenoid

at the position C

as the magnetic field due to magnet is to the right and it is decreasing at the location of the coil ,

hence , the magnetic field due to coil is to the right

the current will flow from 1 to 2 , hence , 1 is positive