# Charges in Magnetic Fields from Surfing Physics book

• alv
In summary, the teacher is trying to answer a question but does not know what the charge on the particle is, how to calculate the force, or how to find the trajectory.
alv
Member advised to use the homework template for posts in the homework sections of PF.
I am a teacher and I can't work this one out. I am trying to answer (a). I have only included the further parts of the question (b, c and d) so you can see why some parts of the question are included.

A single positively charged particle, mass 4.6 x 1027 kg, enters a 4.0 T magnetic field into the page at 2.5 x 106 m/s. The field covers an area of 0.1 m x 0.1 m. It enters at 90 deg, 0.05 m up from the bottom left corner.
(a) Calculate the force on the particle while it is in the field.
(b) Calculate the radius of the path the particle takes in the field.
(c) Calculate the speed with which the particle exits the field.
(d) Where will the particle exit the field?

There is no indication as to what the positive charged particle is. It's too massive for a proton. So I don't know what the charge on it is. I can't see how would be meant to assume that it has the charge of a proton therefore I don't know what the charge is.

I have tried to use F = mv2/r but I don't know the radius.
I could use F = qvB sinθ but as I said, I don't know the charge
I have calculated E from v = E/B so E = vB = 2.5 x 10^6 x 4 = 1 x 10^7 but then I don't know what to do with it.
There is F = BIl sinθ but I don't know what the current is (or length for that matter).

The answer is 1.8 x 10-12 but I don't know how to get it and need to so I can show my students.
Your help would be greatly appreciated.

if I assume one elementary charge the answer comes to 1.6 x 10-12 N?

alv
The information is insufficient. They should mention the charge on the particle.

Also, the mass of the particle given makes it heavier than the earth. I believe the power of 10 should be -27 instead of +27.

alv
If you interpret it as a single positive (elementary) charge on the particle, the answer should be ##1.6\times 10^{-12}## N, as andrevdh wrote. If you don't know the charge nor the trajectory of the particle, it's not possible to calculate the force. And you need the force to calculate the trajectory. But, then, the answer provided is a bit off.

Where did you get E=vB from?

alv
"A single positively charged particle" no doubt means a particle with a single positive elementary charge; There's no reason why they would have to specify that a particle is a single particle.

The mass of the particle, assuming that the power of ten is -27 and not 27 as pointed out by @cnh1995, is 2.75 proton masses, which doesn't strike me as corresponding to anyone known particle. So presumably it's a fabrication by the problem's author.

It's possible that over time the details of the problem's given values have been changed to "refresh" the problem for reuse. We occasionally see examples like this where an answer-key value is incorrect either due to a typo or because it wasn't updated when the problem was revamped.

I suggest that you make reasonable assumptions and from there do the calculations in detail to show your students. The radius of curvature for a charged particle moving in a magnetic field is a well known calculation and comes up often.

alv
Thanks so much for these replies everyone. Much appreciated

## 1. How do charges interact with magnetic fields?

Charges interact with magnetic fields through the Lorentz force, which is a force that acts on a charged particle moving through a magnetic field. This force is perpendicular to both the direction of the particle's motion and the direction of the magnetic field.

## 2. What is the difference between a positive and negative charge in a magnetic field?

A positive charge moving through a magnetic field will experience a force in one direction, while a negative charge moving through the same field will experience a force in the opposite direction. This is due to the fact that positive and negative charges have opposite directions of motion.

## 3. How do charges move in a uniform magnetic field?

In a uniform magnetic field, charges will move in a circular path with a constant speed. This is because the force acting on the charge is always perpendicular to its motion, causing it to change direction but not speed.

## 4. What is the relationship between the strength of the magnetic field and the force on a charge?

The force on a charge in a magnetic field is directly proportional to the strength of the magnetic field and the velocity of the charge. This can be represented by the equation F = qvB, where F is the force, q is the charge, v is the velocity, and B is the magnetic field strength.

## 5. How can the direction of the force on a charge in a magnetic field be determined?

The direction of the force on a charge in a magnetic field can be determined using the right-hand rule. Point your thumb in the direction of the charge's velocity, your fingers in the direction of the magnetic field, and the palm of your hand will face the direction of the force.

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