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.