A rectangular coil of 400 turns on frame of 3cm× 2cm is suspended in magnetic field of induction 0.1 T. A current of 10⁻⁷A flows through the coil. The torque on it in N ^{- m} is

To calculate the torque (τ) on a rectangular coil in a magnetic field, we use the formula

τ = N × I × A × B × sin(θ)

• N: Number of turns in the coil
• I: Current flowing through the coil
• A: Area of the coil
• B: Magnetic field strength
• θ: Angle between the normal to the plane of the coil and the magnetic field

Given Data:

• Number of turns, N = 400
• Dimensions of the coil: length (l) = 3 cm = 0.03 m, width (w) = 2 cm = 0.02 m
• Magnetic field strength, B = 0.1 T
• Current, I = 10^-7 A
• Assuming the coil is oriented for maximum torque, θ = 90°, so sin(θ) = 1

Step 1: Calculate the Area (A) of the Coil

A = l × w = 0.03 m × 0.02 m = 6 × 10^-4 m²

Step 2: Substitute the Values into the Torque Formula

τ = N × I × A × B × sin(90°)

τ = 400 × 10^-7 A × 6 × 10^-4 m² × 0.1 T × 1

Step 3: Simplify

τ = 400 × 10^-7 × 6 × 10^-4 × 0.1

τ = 2.4 × 10^-8 N·m

Final Answer:

The torque on the coil is 2.4 × 10^-8 N·m.