A current of 20 mA flows in a single circular loop with a radius of 2 meters. A uniform magnetic field of 1.2 T points parallel to the plane of the loop. What is the magnitude of the magnetic moment of the loop in A-m^2?
What is the magnitude of the torque on the loop in N-m?
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html
To find the magnitude of the magnetic moment of the loop, we can use the formula:
Magnetic Moment (μ) = Current (I) * Area (A) * Number of Turns (N)
In this case, since there is only one circular loop, the number of turns is 1.
1. Start by finding the area of the circular loop using the formula:
Area (A) = π * (radius)^2
Plugging in the given radius of 2 meters, we get:
Area (A) = π * (2)^2 = 4π square meters
2. Now, let's calculate the magnetic moment using the given current of 20 mA (0.02 A):
Magnetic Moment (μ) = Current (I) * Area (A) * Number of Turns (N)
= 0.02 A * 4π square meters * 1 turn
= 0.08π A-m^2
Therefore, the magnitude of the magnetic moment of the loop is 0.08π A-m^2.
To find the magnitude of the torque on the loop, we can use the formula:
Torque (τ) = Magnetic Moment (μ) * Magnetic Field (B)
In this case, we are given a uniform magnetic field of 1.2 T.
3. Substitute the values into the formula:
Torque (τ) = Magnetic Moment (μ) * Magnetic Field (B)
= 0.08π A-m^2 * 1.2 T
Evaluating the expression gives:
Torque (τ) = 0.096π N-m
Therefore, the magnitude of the torque on the loop is approximately 0.096π N-m.