Torque on a charged particle moving in a circle in a uniform B field

[ganondorf29]

Homework Statement

A particle of charge q = e moves in a circle of radius = 0.44 m with speed v = 2.350×107 m/s. Treating the circular path as a current loop with constant current equal to its average current, find the maximum torque exerted on the loop by a uniform magnetic field of magnitude B = 1.00 T.

Homework Equations

R=mv/qB

The Attempt at a Solution

I'm stuck and I don't really know where to go. I did find the mass by the following equation:
m = rqB / v
m = 0.44 * 1.602E-19 * 1 / 2.35E7
m = 2.999E-27 kg

I could also find KE but I'm not sure what to do with either of these two. How does torque relate to magnetism?

 

[Doc Al]

I'm stuck and I don't really know where to go. I did find the mass by the following equation:
m = rqB / v
m = 0.44 * 1.602E-19 * 1 / 2.35E7
m = 2.999E-27 kg

You are solving a different problem. Realize that the given magnetic field is not the field that is making the charge go in a circle.

Treat the moving charge as a current loop. (What's the average current?) A current loop placed in a magnetic field will experience a torque. Look up: torque on a current loop, magnetic moment of a current loop.

 

[nlightner]

I can provide some guidance on how to approach this problem. First, it is important to understand the concept of torque and how it relates to magnetism. Torque is a measure of the rotational force applied to an object, and it is calculated by multiplying the force applied by the distance from the axis of rotation. In the case of a charged particle moving in a circle, the force is the Lorentz force, which is given by F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field.

Now, to find the torque exerted on the particle, we need to find the distance from the axis of rotation. In this case, the radius of the circle is given as 0.44 m, so the distance from the axis of rotation would be half of that, or 0.22 m. Therefore, the torque would be given by T = qvBd, where d is the distance from the axis of rotation.

Next, we need to determine the maximum torque that can be exerted on the particle. This would occur when the Lorentz force is perpendicular to the velocity of the particle, which means that the angle between the force and the distance from the axis of rotation would be 90 degrees. In this case, the maximum torque would be given by T = qvBd = qvB(0.22) = 0.22qBv.

Now, we can plug in the given values to calculate the maximum torque. We know that q = e (charge of an electron), v = 2.350×107 m/s, and B = 1.00 T. Plugging these values in, we get T = (1.602E-19)(2.350×107)(1.00)(0.22) = 7.45E-12 Nm.

In conclusion, the maximum torque exerted on the charged particle by the uniform magnetic field is 7.45E-12 Nm. It is important to note that this torque is only applicable when the particle is moving in a circle, and it will vary as the particle moves along different paths.