Question

You have a wire of length L = 0.8 m for making a square coil of a dc motor. The current in the coil is I = 2.1 A, and the magnetic field of the motor has a magnitude of B = 0.18 T. Find the maximum torque exerted on the coil when the wire is used to make (a) a single-turn square coil and (b) a two-turn square coil.

Answer 1

Length of th ewire L = 0.8 m

i.e., circumference of the square coil = L

                              4 a = L

From this side of the square a = L / 4

                                             = 0.2 m

Area of square A = a ²

                         = 0.04 m ²

Current in the coil i = 2.1 A

Magnitude of the magnetic field B = 0.18 T

(a). The maximum torque exerted on the coil when the wire is used to make a single-turn square coil

                      = B i A

                      = 0.01512 N m

(b) when the wire is used to make a two-turn square coil then

circumference of the each square coil = L / 2

                              4 a '= L / 2

From this side of the square a ' = L / 8

                                             = 0.1 m

Area of square A '= a ²

                         = 0.01 m ²

The maximum torque exerted on the coil when the wire is used to make a two-turn square coil

                      = NB i A '

Where N = number of truns = 2

                      = 0.00756 N m