A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30° with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
Given:
Length of side of square, L = 10 cm
Number of turns, n = 20
Current through the square coil, I = 12 A
Angle between the normal to the coil and uniform magnetic field, θ = 30°
Magnitude of magnetic field, B = 0.80 T
The torque experienced by the coil in a magnetic field is given by,
T = n × B × I × A × sin(θ) …(1)
Where,
n = number of turns
B = Strength of magnetic field
I = Current through the coil
A = Area of cross-section of coil
A = L2 = 0.1 × 0.1 = 0.01m2 …(2)
θ = Angle between normal to cross-section of coil and magnetic field
Now by plugging the values in equation (1), we get
T = 20 × 0.80T × 12A × 0.01m2 × sin30°
⇒ T = 0.96 Nm
∴ the magnitude torque experienced by the coil is 0.96 N-m.
Hence the torque experienced by the square coil is 0.96 Nm.