Work on a proton in uniform magnetic field

• Elbobo
In summary, the magnetic field forces the protons to move in a circle of radius 0.1 m with the plane of the circle perpendicular to the magnetic field. The work done by the magnetic field on the protons is estimated to be 7.67235874 x 10^-16 J.
Elbobo

Homework Statement

A magnetic field of 0.1 T forces a proton beam
of 1.5 mA to move in a circle of radius 0.1 m.
The plane of the circle is perpendicular to the
magnetic field.
Of the following, which is the best estimate
of the work W done by the magnetic field on
the protons during one complete orbit of the
circle?
1. W = 0 J
2. W = 10^22 J
3. W = 10^−22 J
4. W = 10^20 J
5. W = 10^−5 J

F = qVB = ILB
F = mv^2 / r
C = 2 pi*r

The Attempt at a Solution

Since work is energy, I used the formula for kinetic energy...

W = 1/2 mv^2

Fcentripetal = Fmagnetic
mv^2 /r = qvB
v = rqB / m

W = 1/2 m (rqB / m)^2
W = 1/2 (1.6725 x 10^-27) * (0.1 * 1.602 x 10^-19 * 0.1 / 1.6725 x 10^-27) ^2
W = 7.67235874 x 10^-16 J

This isn't close to any of the answer choices. Can someone help me?

Last edited:
The Force supplied by the B field is

F = qV X B (the cross product)

What is the direction of this force relative to the direction of the motion of the particle?

Isn't Work

W = F ⋅ D (the dot product)

I tried a multitude of ways, including that, and the order was between -13 and -17. The closest answer to that is choice 3, but that's wrong.

F = qvB
W = qvB * 2 pi r

(in part 2, I solved for v and found that it's approximately 10^6)

W = (1.602 x 10-19) (10^6) (0.1) * 2 pi * 0.1
W = 1.00656629 x 10^-14 J

Again, nothing close.

OR, does anyone think choice 5 is a typo, and it meant to be 10^-15?

My online system sometimes has problems/answers like that unfortunately...

What angle is the B field and the Force making with the direction of motion?

Everything is at a right angle.

So how much work does a force at right angle do again?

Work is F⋅D which is the dot product.

So what is the dot product of the Force with the direction of motion?

Ohhh, so it's zero. Gah, I was supposed to remember that detail from that chapter we learned months ago.

Thanks again for all your help, LowlyPion.

1. What is a proton?

A proton is a subatomic particle with a positive charge that is found in the nucleus of an atom. It is one of the building blocks of matter, along with neutrons and electrons.

2. What is a uniform magnetic field?

A uniform magnetic field is a region of space where the magnetic field has the same strength and direction at every point. It is often represented by evenly spaced magnetic field lines that are parallel to one another.

3. How does a proton behave in a uniform magnetic field?

In a uniform magnetic field, a proton will experience a force that is perpendicular to both its velocity and the direction of the magnetic field. This force will cause the proton to move in a circular path, known as a cyclotron motion.

4. What is the significance of studying a proton in a uniform magnetic field?

Studying the behavior of a proton in a uniform magnetic field can help us understand the fundamental properties of matter and the interactions between particles. It also has practical applications in fields such as medical imaging and particle accelerators.

5. How is the motion of a proton affected by changing the strength of the magnetic field?

As the strength of the magnetic field increases, the radius of the proton's circular path will decrease, and its speed will increase. This is because the force acting on the proton is directly proportional to the strength of the magnetic field.

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