What is the maximum torque on a current loop in a magnetic field?

In summary, we can use the formula τ = μB (sinθ) to determine the maximum torque on a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of motion. By substituting in the values given for the radius, speed, and magnetic field, we can calculate the maximum torque to be 6.59 x 10^-26 N*m.
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Splatapus
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Homework Statement


An electron moves in a circle of radius r = 5.29 x 10^-11 m with speed 2.19 x 10^6 m/s. Treat the circular path as a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of the motion. If the circle lies in a uniform magnetic field of magnitude B = 7.10 mT, what is the maximum possible magnitude of the torque produced on the loop by the field?


Homework Equations





The Attempt at a Solution



Here's my attempt, could you tell me if it is the correct approach?
Ok, so we can use τ(tao) = μB (sinθ). Since we are trying to figure out the maximum torque, then it must appear at 90 degrees since (sin 90) = 1.
So now we replace μ with μ=NiA, where i is current, A is area, and N is the number of coils. Here, N is 1 since there is only 1 loop.
Now we need to determine current. As the question states, current is the ratio of electron charge and period of motion. Period is T = circumference/speed. T = 2∏r/2.19 x 10^6 = 1.5177 s. Then i = q/T, so i = 1.602 x 10-19 / 1.5177 = 0.001055531 A.
Sub "i" back into τ=iAB = (0.001055531)(∏)(5.29 x 10 ^-11)(5.29 x 10^-11)(7.1 x 10 ^-3) = 6.59 x 10^-26 N*m
 
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  • #2
. So the maximum possible magnitude of the torque produced on the loop by the field is 6.59 x 10^-26 N*m.
 

1. What is torque on a current loop?

Torque on a current loop is a measure of the rotational force that is exerted on a loop of wire carrying an electric current when placed in a magnetic field.

2. How is torque on a current loop calculated?

The formula for calculating torque on a current loop is T = N * I * A * B * sin(theta), where T is torque, N is the number of turns in the loop, I is the current, A is the area of the loop, B is the magnetic field strength, and theta is the angle between the direction of the current and the magnetic field.

3. What is the direction of torque on a current loop?

The direction of torque on a current loop is perpendicular to both the direction of the current and the direction of the magnetic field, according to the right-hand rule.

4. How does the orientation of a current loop affect torque?

The orientation of a current loop can affect the magnitude and direction of torque. If the plane of the loop is parallel to the magnetic field, there will be no torque. However, if the plane of the loop is perpendicular to the magnetic field, there will be maximum torque.

5. What are some real-life applications of torque on a current loop?

Torque on a current loop is important in the functioning of electric motors, generators, and other devices that use electromagnetic principles. It is also used in instruments such as galvanometers and magnetic compasses.

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