A square loop of wire of side 3.0 cm carries 3.0 A of current. A uniform magnetic field of magnitude 0.67 T makes an angle of 37degree with the plane of the loop. What is the magnitude of the torque on the loop? 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, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the magnetic field and the plane of the loop.

Let's calculate it step by step:

1. Calculate the area of the loop:
The area of a square is given by A = side * side.
In this case, the side length of the square loop is 3.0 cm, so the area is A = 3.0 cm * 3.0 cm.

2. Convert the area to square meters:
To work with SI units, we need to convert the area to square meters.
1 cm^2 = (1 cm/100 m)^2 = 1e-4 m^2.
So the area in square meters is A = (3.0 cm * 3.0 cm) * 1e-4 m^2.

3. Calculate the torque:
Plugging in the given values, we get:
τ = (3.0 A) * (3.0 cm * 3.0 cm * 1e-4 m^2) * (0.67 T) * sin(37°).

Now, to calculate the net magnetic force on the loop, we can use the formula:

F = I * L * B * sin(θ)

where F is the force, I is the current, L is the length of wire in the loop, B is the magnetic field strength, and θ is the angle between the magnetic field and the plane of the loop.

Let's calculate it step by step:

1. Calculate the length of the wire:
Since the wire is a square loop, the length of wire in each side of the loop is equal to the perimeter of the square.
The perimeter of a square is given by P = 4 * side.
In this case, the side length of the square loop is 3.0 cm, so the length of wire is L = 4 * 3.0 cm.

2. Convert the length to meters:
To work with SI units, we need to convert the length to meters.
1 cm = 1e-2 m.
So the length in meters is L = 4 * 3.0 cm * 1e-2 m.

3. Calculate the force:
Plugging in the given values, we get:
F = (3.0 A) * (4 * 3.0 cm * 1e-2 m) * (0.67 T) * sin(37°).

Now you can use a calculator to find the values of τ and F.