6.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?

b. What is the magnitude of the torque on the loop in N-m?

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

Magnetic Moment (m) = Current (I) * Area (A) * Number of Turns (N)

The current is given as 20 mA, which is equal to 0.02 A.

The area of a circle is given by the formula, A = π * r^2, where r is the radius of the loop.

The radius is given as 2 meters, so the area is A = π * (2)^2 = 4π m^2.

Since there is only one loop, the number of turns (N) is 1.

Thus, the magnetic moment is:

m = 0.02 A * 4π m^2 * 1 = 0.08π A-m^2

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

Torque (τ) = Magnetic Moment (m) * Magnetic Field (B) * sin(θ)

The magnetic field is given as 1.2 T (Tesla), and it points parallel to the plane of the loop.

The angle (θ) between the magnetic moment and the magnetic field is 90 degrees, as they are parallel.

So, sin(90°) = 1.

Therefore, the torque is:

τ = 0.08π A-m^2 * 1.2 T * 1 = 0.096π N-m

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

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

Magnetic Moment (μ) = Current (I) * Area (A)

In this case, the current flowing through the loop is given as 20 mA. To convert it to Amperes, we divide it by 1000:

I = 20 mA / 1000 = 0.02 A

The area of a circular loop is given by the formula:

Area (A) = π * (radius)^2

Here, the radius is given as 2 meters, so we have:

A = π * (2)^2 = 4π m^2

Now we can calculate the magnitude of the magnetic moment:

μ = I * A = 0.02 A * 4π m^2

μ ≈ 0.08π A-m^2 (approximately)

Therefore, the magnitude of the magnetic moment of the loop is approximately 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) * Sin(θ)

In this case, the magnetic field is given as 1.2 T and the angle between the magnetic moment and the magnetic field (θ) is 90 degrees, as they are parallel to each other.

τ = μ * B * Sin(θ) = 0.08π A-m^2 * 1.2 T * Sin(90°)

Sin(90°) = 1, so the equation simplifies to:

τ = 0.08π A-m^2 * 1.2 T * 1 = 0.096π N-m

Therefore, the magnitude of the torque on the loop is approximately 0.096π N-m.