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?

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?

magnetic moment= current(I)* area(A)

= 20*10^-3* pi*2^2
= 0.2513

torque= magnetic moment*magnetic field(B)
= 0.2513*1.2
=0.301

To find the magnitude of the magnetic moment of the loop (μ), we can use the formula:

μ = I * A

where:
I = current flowing through the loop in Amperes (A)
A = area of the loop in square meters (m^2)

First, we need to find the area of the loop using the formula:

A = π * r^2

where:
π = pi (approximately 3.14159)
r = radius of the loop in meters (m)

Given that the radius of the loop is 2 meters, we can substitute the values into the formula:

A = π * 2^2
A = 4π

Now, we can find the magnitude of the magnetic moment by multiplying the current and the area:

μ = 20 mA * 4π

Since the current is given in milliamperes (mA), we need to convert it to Amperes (A) by dividing by 1000:

μ = (20 mA / 1000) * 4π

Simplifying further:

μ = 0.02A * 4π

μ ≈ 0.08π A-m^2 (rounded to two decimal places)

To find the magnitude of the torque on the loop (τ), we can use the formula:

τ = μ * B * sin(θ)

where:
μ = magnetic moment of the loop in A-m^2
B = magnetic field strength in Tesla (T)
θ = angle between the magnetic moment and the magnetic field direction (in this case, sin(θ) = 1 because the magnetic field is parallel to the plane of the loop)

Given that the magnetic field strength is 1.2 T and sin(θ) = 1, we can substitute the values into the formula:

τ = 0.08π A-m^2 * 1.2 T * 1

Simplifying:

τ ≈ 0.096π N-m (rounded to two decimal places)

Therefore, the magnitude of the magnetic moment of the loop is approximately 0.08π A-m^2, and the magnitude of the torque on the loop is approximately 0.096π N-m.