Question

A wire 80 cm long carries 11 A of current. From this wire, a loop of 90-turns is made and placed in a magnetic field of 6.50 Tat an angle of 35˚. In first experiment, a square loop is formed and in the second experiment, a circular loop is formed with same number of turns. Calculate the torque in each loop. Which loop produces more torque-the circular loop or the square loop? What is the reason for this change of torque in both loops?   

Answer 1

Solution :

Given :

Length of wire (L) = 80 cm = 0.80 m

Current through the wire (I) = 11 A

Number of loops (N) = 90

Magnetic field (B) = 6.50 T

Angle () = 35˚

.

Here, radius of circular loop will be : (r) = L / (N x 2) = 0.80 m / (90 x 2) = 0.0014 m

So, Area of Circular loop (A) = r² = (0.0014 m)² = 6.288 x 10^-6 m²

Therefore: Torque on Circular loop = N I B A sin = (90)(11 A)(6.50 T)(6.288 x 10^-6 m²) sin(35˚) = 0.0232 Nm

.

Here, Length of sides of Square loop will be : (a) = L / (N x 4a) = 0.80 m / (90 x 4) = 0.0022 m

So, Area of Square loop (A) = a² = (0.0022 m)² = 4.938 x 10^-6 m²

Therefore: Torque on Square loop = N I B A sin = (90)(11 A)(6.50 T)(4.938 x 10^-6 m²) sin(35˚) = 0.0182 Nm