A wire has a length of 5.40 10-2 m and is used to make a circular coil of one turn. There is a current of 2.30 A in the wire. In the presence of a 3.80-T magnetic field, what is the maximum torque that this coil can experience?

To find the maximum torque experienced by the coil, you need to use the formula for the torque on a current-carrying loop in a magnetic field.

The formula for torque on a current-carrying loop in a magnetic field is:

τ = N * I * A * B * sin(θ)

where:
τ is the torque on the loop,
N is the number of turns in the loop,
I is the current in the loop,
A is the area of the loop,
B is the magnetic field, and
θ is the angle between the magnetic field and the normal to the loop.

In this case, we have a circular coil with one turn, a current of 2.30 A, and a magnetic field of 3.80 T.

To calculate the maximum torque, we need to determine the area of the loop and the angle between the magnetic field and the normal to the loop.

The area of a circular loop is given by the formula:

A = π * r^2

where r is the radius of the loop.

The radius of the loop can be found from the length of the wire. Since the wire is used to make a circular coil with one turn, the circumference of the loop is equal to the length of the wire. Thus, the formula for the circumference of a circle gives us:

2πr = 5.40 * 10^-2 m

Solving for r, we get:

r = (5.40 * 10^-2 m) / (2π)

Now, we can use the formula for the area to calculate the area of the loop:

A = π * ((5.40 * 10^-2 m) / (2π))^2

Simplifying, we find:

A = (5.40 * 10^-2 m)^2 / (4 * π)

Next, we need to find the angle between the magnetic field and the normal to the loop. In this case, since the loop is flat and the field is perpendicular to it, the angle is 90 degrees (π / 2 radians).

Now we have all the values we need to calculate the maximum torque. Plugging the values into the formula, we get:

τ = (1 turn) * (2.30 A) * (5.40 * 10^-2 m)^2 / (4 * π) * (3.80 T) * sin(π/2)

Simplifying, we find:

τ = (1 turn) * (2.30 A) * (5.40 * 10^-2 m)^2 / (4 * π) * (3.80 T)

Evaluating the expression, we get:

τ ≈ 1.28 * 10^-4 N•m

Therefore, the maximum torque experienced by the coil is approximately 1.28 * 10^-4 N•m.