A current loop in a motor has an area of 0.85 cm^2. It carries a 240 mA current in a uniform field of 0.62 T. What is the magnitude of the maximum torque on the current loop?
To find the magnitude of the maximum torque on the current loop, we can use the formula:
τ = N * A * B * sin(θ)
where:
τ is the torque,
N is the number of turns in the loop,
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.
In this case, we are given the following information:
A = 0.85 cm^2 (area of the loop)
I = 240 mA = 0.240 A (current in the loop)
B = 0.62 T (uniform magnetic field)
We need to find the value of N, the number of turns in the loop, and θ, the angle between the magnetic field and the plane of the loop.
The number of turns, N, is not provided, so we will assume it as 1 (a single loop). As a result, N = 1.
The angle, θ, between the magnetic field and the plane of the loop is not specified in the question. However, if we assume the magnetic field is perpendicular to the plane of the loop, then θ = 90 degrees. In this case, sin(θ) = sin(90) = 1.
Inserting the known values into the formula:
τ = N * A * B * sin(θ)
= 1 * 0.85 cm^2 * 0.62 T * 1
To calculate the torque, we need to convert cm^2 to m^2 since the SI unit for area is square meters.
1 cm^2 = (1/100)^2 m^2 = 0.0001 m^2
Now, plugging in the values:
τ = 1 * 0.0001 m^2 * 0.62 T * 1
Simplifying:
τ = 0.000062 Nm
Hence, the magnitude of the maximum torque on the current loop is 0.000062 Nm.