A square loop of wire of side 2.8 cm carries 3.0 A of current. A uniform magnetic field of magnitude 0.67 T makes an angle of 43° with the plane of the loop.
(a) What is the magnitude of the torque on the loop?
(b) What is the net magnetic force on the loop?
To find the magnitude of the torque on the loop, we can use the formula:
τ = I * A * B * sin(θ)
Where:
- τ is the torque
- I is the current flowing through the wire
- A is the area of the loop
- B is the magnitude of the magnetic field
- θ is the angle between the magnetic field and the plane of the loop
To find the area of the loop, we can square the side length of the loop:
A = (side length)^2
Let's calculate the values step by step:
(a) Finding the magnitude of the torque:
- I = 3.0 A (given)
- side length = 2.8 cm = 0.028 m
- A = (0.028 m)^2 = 0.000784 m^2 (calculate)
- B = 0.67 T (given)
- θ = 43° (given)
Substituting the values into the formula:
τ = 3.0 A * 0.000784 m^2 * 0.67 T * sin(43°) (calculate)
(b) To find the net magnetic force on the loop, we can use the formula:
F = I * A * B * sin(θ)
Using the same values for I, A, B, and θ:
F = 3.0 A * 0.000784 m^2 * 0.67 T * sin(43°) (calculate)
Using these formulas and calculations, you can find the magnitude of the torque on the loop (a) and the net magnetic force on the loop (b).