A 35 turn coil of radius 4.9 cm rotates in a uniform magnetic field having a magnitude of 0.53 T. If the coil carries a current of 20 mA, find the magnitude of the maximum torque exerted on the coil.
To find the magnitude of the maximum torque exerted on the coil, we can use the formula for torque in a magnetic field:
T = N * B * A * sin(θ)
Where:
T is the torque,
N is the number of turns in the coil (35 turns),
B is the magnetic field strength (0.53 T),
A is the area of the coil,
and θ is the angle between the magnetic field and the plane of the coil.
First, let's calculate the area of the coil. The coil is circular with a radius of 4.9 cm, so the area is given by:
A = π * r^2
Substituting the radius into the formula, we get:
A = π * (0.049 m)^2
Next, we need to convert the current from mA to Amperes:
I = 20 mA = 20 * 10^-3 A
Now we have all the values we need. Let's calculate the maximum torque:
T = (35) * (0.53 T) * (π * (0.049 m)^2) * sin(θ)
Since the orientation of the coil is not specified, the angle θ is assumed to be 90 degrees, which means sin(θ) = 1.
T = (35) * (0.53 T) * (π * (0.049 m)^2) * 1
Simplifying further:
T = 35 * 0.53 * π * (0.049)^2
Using a calculator to evaluate the expression, we find:
T ≈ 0.170 N*m
Therefore, the magnitude of the maximum torque exerted on the coil is approximately 0.170 N*m.