Final answer:
The magnetic induction, or magnetic field strength (B), acting on the coil with maximum torque of 4×10⁻⁸ Nm, coil's effective area of 0.04 m², and current of 10µA is 0.1 Tesla (T) assuming the coil has one turn and the angle θ is 90 degrees.
Step-by-step explanation:
To calculate the magnetic induction (also known as magnetic field strength, B) acting on a coil when given the maximum torque (τ), the coil's effective area (A), and the current (I), we can use the formula for torque on a current-carrying loop in a magnetic field:
τ = n * B * I * A * sin(θ)
Where:
- τ is the torque
- n is the number of turns in the coil (which is not provided in your question and would generally default to 1 unless otherwise specified)
- B is the magnetic field strength
- I is the current
- A is the area of the coil
- θ is the angle between the magnetic field and the normal to the coil's plane (for maximum torque, θ = 90° or π/2 radians)
Since we are looking for the maximum torque, we assume that sin(θ) = sin(90°) = 1. Substituting the known values and solving for B:
4×10⁻⁸ Nm = n * B * 10⁻⁶ A * 0.04m² * 1
Solving for B, assuming n = 1:
B = τ / (I * A)
B = 4×10⁻⁸ Nm / (10⁻⁶ A * 0.04 m²)
B = 0.1 Tesla (T)
The magnetic induction acting on the coil is 0.1 T given the stated conditions for maximum torque.