A circular coil of radius 40mm is found to produce a field 12.1 × 10^-6T at a point 30mm along its axis.
1- What is the electromagnetic moment?
2- What maximum torque could it experience in a uniform magnetic field of 3.0×10^-3T?
Answer 356
To find the electromagnetic moment of a circular coil, you can use the formula:
M = B * A
1. Where:
M is the electromagnetic moment,
B is the magnetic field strength, and
A is the area of the coil.
Given that the radius of the coil (r) is 40mm, the area of the coil (A) can be calculated as follows:
A = π * r^2
Substituting the known values:
A = π * (0.04m)^2
A = π * 0.0016
A ≈ 0.005026548 m^2
Now, we can find the electromagnetic moment (M) by multiplying the magnetic field strength (B) by the area (A):
M = 12.1 × 10^-6T * 0.005026548 m^2
M ≈ 6.11 × 10^-8 Am^2
Therefore, the electromagnetic moment is approximately 6.11 × 10^-8 Am^2.
To calculate the maximum torque (τ) experienced by the circular coil in a uniform magnetic field, you can use the formula:
τ = M * B
2. Where:
τ is the torque,
M is the electromagnetic moment, and
B is the magnetic field strength.
Given that the magnetic field strength (B) is 3.0 × 10^-3T, we can substitute the known values to find the maximum torque (τ):
τ = 6.11 × 10^-8 Am^2 * 3.0 × 10^-3T
τ ≈ 1.83 × 10^-10 Nm
Therefore, the maximum torque that the circular coil could experience in a uniform magnetic field of 3.0 × 10^-3T is approximately 1.83 × 10^-10 Nm.
To find the electromagnetic moment of a circular coil, you can use the formula:
Magnetic Moment (m) = B × A
where B is the magnetic field and A is the area of the coil.
1- To calculate the electromagnetic moment:
Step 1: Calculate the area of the circular coil.
A = π × r^2
= π × (40mm)^2
= π × 1600mm^2
(Note: Keep the value of π for further calculations)
Step 2: Convert the radius from millimeters to meters.
r = 40mm × (1m/1000mm) = 0.04m
Step 3: Calculate the magnetic moment.
m = B × A
= (12.1 × 10^-6T) × (π × 0.04^2m^2)
You can now plug in the values and solve the equation to find the magnetic moment.
2- To calculate the maximum torque experienced by the coil in a uniform magnetic field, you can use the formula:
Torque (τ) = m × B
where m is the magnetic moment and B is the magnetic field.
Step 1: Convert the magnetic field from Tesla to Gauss (1T = 10,000G).
B = 3.0 × 10^-3T × 10,000G/T
Step 2: Plug in the values and calculate the maximum torque.
τ = m × B
By substituting the value of m from the previous calculation, you can find the maximum torque experienced by the coil in the uniform magnetic field.