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, we can use the equation:

Torque = N * I * A * B * sin(θ)

where
N is the number of turns,
I is the current flowing through the coil,
A is the area of the coil, and
B is the magnetic field strength.

For a circular coil of one turn, the area of the coil (A) is given by:

A = π * r^2

where r is the radius of the coil.

Let's find the radius of the coil first. The length of the wire (L) is given as 5.40 x 10^-2 m, and for a circular coil of one turn, the circumference (C) is equal to the length of the wire:

C = 2 * π * r

Solving for r, we get:

r = L / (2 * π)

Substituting the value of L, we get:

r = 5.40 x 10^-2 / (2 * π)

Now, we can find the area of the coil (A) using the formula mentioned above:

A = π * (5.40 x 10^-2 / (2 * π))^2

Simplifying, we have:

A = (5.40 x 10^-2)^2 / (2 * π)

N is given as one turn, and the current (I) is 2.30 A. The magnetic field (B) is given as 3.80 T.

Lastly, we have to consider the angle (θ) between the direction of the magnetic field and the plane of the coil. Assuming the field is perpendicular to the plane of the coil, sin(θ) is equal to 1.

Substituting all the values into the torque equation:

Torque = 1 * 2.30 * [(5.40 x 10^-2)^2 / (2 * π)] * 3.80 * 1

Simplifying further, we can calculate the maximum torque experienced by the coil.