A current loop with radius 20 cm and current 2 A is in a uniform magnetic field of 0.5 T. Considering all possible orientations of the loop relative to the field, what is the largest potential energy difference (in Joules) you can find between two orientations?
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?
To find the largest potential energy difference between two orientations of the loop, we need to consider the change in potential energy when the loop is rotated in the magnetic field.
The potential energy (U) of a current loop in a magnetic field is given by the equation:
U = -m * B * cos(theta)
Where:
- U is the potential energy
- m is the magnetic moment of the loop (equal to the product of the current and the area of the loop)
- B is the magnetic field strength
- theta is the angle between the magnetic moment vector and the magnetic field vector
In this case, we are given the radius of the loop (r = 20 cm) and the current through the loop (I = 2 A).
To calculate the magnetic moment of the loop, we use the equation:
m = I * A
The area (A) of a circular loop is given by the equation:
A = π * r^2
Substituting the values, we can find the magnetic moment (m):
m = I * A = 2 A * π * (0.2 m)^2
Now we can calculate the potential energy (U) for two different orientations of the loop.
First, let's consider the orientation where the loop is perpendicular to the magnetic field (theta = 90 degrees):
U1 = -m * B * cos(90) = 0 (as cos(90) = 0)
Next, let's consider the orientation where the loop is parallel to the magnetic field (theta = 0 degrees):
U2 = -m * B * cos(0) = -m * B
Substituting the magnetic moment (m) and the magnetic field strength (B) into the equation, we get:
U2 = - (2 A * π * (0.2 m)^2) * 0.5 T
Now, we can calculate the difference in potential energy between these two orientations:
Delta U = U2 - U1 = - (2 A * π * (0.2 m)^2) * 0.5 T - 0
Simplifying, we find:
Delta U = - (2 A * π * (0.2 m)^2) * 0.5 T
Calculating this expression will give us the largest potential energy difference between the two orientations of the loop in joules.