To find the torque acting on a circular loop in a magnetic field, you're on the right track with the formula you mentioned. However, let's clarify the variables and ensure we apply them correctly. The torque (\( \tau \)) on a current-carrying loop in a magnetic field can be calculated using the formula:
Understanding the Torque Formula
The formula for torque is given by:
τ = N * I * A * B * sin(θ)
- N = number of turns in the loop
- I = current flowing through the loop (in Amperes)
- A = area of the loop (in square meters)
- B = magnetic field strength (in Teslas)
- θ = angle between the magnetic field and the normal (perpendicular) to the loop (in degrees)
Calculating the Area of the Loop
First, we need to calculate the area (\( A \)) of the circular loop. The area of a circle is given by the formula:
A = π * r²
Given that the radius \( r \) is 0.0200 m, we can calculate:
A = π * (0.0200 m)² ≈ 3.14 * 0.0004 m² ≈ 0.00125664 m²
Substituting Values into the Torque Formula
Now that we have the area, we can substitute all the known values into the torque formula:
- N = 60 turns
- I = 0.358 A
- A ≈ 0.00125664 m²
- B = 0.259 T
- θ = 52.0 degrees
Before substituting, we need to convert the angle from degrees to radians since many calculators use radians. However, since we are using the sine function, we can directly use the sine of the angle in degrees:
Now, we can calculate:
τ = 60 * 0.358 A * 0.00125664 m² * 0.259 T * sin(52.0°)
Calculating \( \sin(52.0°) \) gives approximately 0.7880. Now substituting this value in:
τ ≈ 60 * 0.358 * 0.00125664 * 0.259 * 0.7880
Calculating this step-by-step:
- 60 * 0.358 ≈ 21.48
- 21.48 * 0.00125664 ≈ 0.02698
- 0.02698 * 0.259 ≈ 0.006986
- 0.006986 * 0.7880 ≈ 0.0055 N·m
Final Result
Thus, the torque acting on the loop is approximately:
τ ≈ 0.0055 N·m
This value represents the torque exerted on the loop due to the interaction of the current and the magnetic field at the specified angle. If you have any further questions or need clarification on any of these steps, feel free to ask!
