A 47.5-turn circular coil of radius 5.15 cm can be oriented in any direction in a uniform magnetic field having a magnitude of 0.490 T. If the coil carries a current of 22.9 mA, find the magnitude of the maximum possible torque exerted on the coil.
_______N*m?
oho
To find the magnitude of the maximum possible torque exerted on the coil, you can use the formula for the torque on a current-carrying coil in a magnetic field:
Torque (τ) = N * B * A * sin(θ)
Where:
N = number of turns in the coil
B = magnetic field strength
A = area of the coil
θ = angle between the magnetic field and the plane of the coil
First, let's calculate the area of the coil. The area of a circle is given by the formula:
A = π * r^2
Where:
r = radius of the coil
Given that the radius of the coil is 5.15 cm, we can substitute this value into the formula and calculate the area:
A = π * (5.15 cm)^2
Next, we need to convert the radius to meters, as the magnetic field strength is given in Tesla (T), which is the SI unit. There are 100 cm in a meter, so the radius in meters is:
r = 5.15 cm / 100 = 0.0515 m
Substituting this value into the equation for the area, we get:
A = π * (0.0515 m)^2
Now, we know the number of turns in the coil (N = 47.5), the magnetic field strength (B = 0.490 T), and the area of the coil (A = π * (0.0515 m)^2). The only unknown in the equation is the angle θ, which represents the orientation of the coil with respect to the magnetic field.
Since the question states that the coil can be oriented in any direction, we need to consider the worst-case scenario for torque. In this case, the angle between the magnetic field and the plane of the coil is 90 degrees, which is the maximum value for sin(θ).
Now, we can calculate the torque:
τ = N * B * A * sin(90 degrees)
Substituting the values we have:
τ = 47.5 * 0.490 T * π * (0.0515 m)^2 * sin(90 degrees)
Remember that sin(90 degrees) = 1, so we can simplify the equation further:
τ = 47.5 * 0.490 T * π * (0.0515 m)^2 * 1
Now, we can perform the calculations to find the magnitude of the maximum possible torque on the coil.