# Relation between magnetic and electric fields

## Homework Statement

What is the electric field strength at the position of the proton in the figure?(Figure 1) Assume that B = 0.10 T and F = 3.4×10−13N .

Figure 1: https://session.masteringphysics.com/problemAsset/1385081/6/35.P29.jpg

## Homework Equations

Honestly I don't know. Since we have a velocity, b-field, and force i thought F=qvXb but that doesnt help with solving the electric field. Other than that I really don't know.

## The Attempt at a Solution

I really havent even been able to start. I have no idea how to approach the problem.

berkeman
Mentor

## Homework Statement

What is the electric field strength at the position of the proton in the figure?(Figure 1) Assume that B = 0.10 T and F = 3.4×10−13N .

Figure 1: https://session.masteringphysics.com/problemAsset/1385081/6/35.P29.jpg

## Homework Equations

Honestly I don't know. Since we have a velocity, b-field, and force i thought F=qvXb but that doesnt help with solving the electric field. Other than that I really don't know.

## The Attempt at a Solution

I really havent even been able to start. I have no idea how to approach the problem.
Welcome to the PF.

The Relevant Equation is the Lorentz Force. Look that up in your study materials or Google it online, and then start filling in the known quantities to solve for the unknown E field strength and direction. Welcome to the PF.

The Relevant Equation is the Lorentz Force. Look that up in your study materials or Google it online, and then start filling in the known quantities to solve for the unknown E field strength and direction. So I use F = qE + qvXB, they give me the v, B, F, and q since it is a proton. Then i just solve for E right? Where would the angle of 30degrees come in to play?

berkeman
Mentor
So I use F = qE + qvXB, they give me the v, B, F, and q since it is a proton. Then i just solve for E right? Where would the angle of 30degrees come in to play?
Good! The Lorentz Force equation is a vector equation. Are you able to solve it using vectors?

Good! The Lorentz Force equation is a vector equation. Are you able to solve it using vectors?

Ah ok, i got it, thank you.

I know this post was 4 years ago, but I'm working on a similar problem, and I can't seem to figure out how to do it with vectors. I have all the numbers needed, but I can't figure out where to use the 30 degrees

berkeman
Mentor
I know this post was 4 years ago, but I'm working on a similar problem, and I can't seem to figure out how to do it with vectors. I have all the numbers needed, but I can't figure out where to use the 30 degrees
Welcome to PhysicsForums. Define your x,y,z coordinate system (label the diagram), and write your vector Lorentz force equation. Can you show us that much? And then you just solve that equation -- you have the vector resultant force on the lefthand side (LHS) of the equation, and you have the electric force vector and magnetic force vector terms on the RHS...

• blank_L14
Welcome to PhysicsForums. Define your x,y,z coordinate system (label the diagram), and write your vector Lorentz force equation. Can you show us that much? And then you just solve that equation -- you have the vector resultant force on the lefthand side (LHS) of the equation, and you have the electric force vector and magnetic force vector terms on the RHS...

For the problem that I'm working on, F=2.4x10^-13 N and B=.17 T, the velocity is the same, and it's an electron. So the equation would be
F=qv x B + qE
I understand that much, but the angle between v and B is 90, so it just goes to qvB because sin(90)=1.
I know qE has to have some vector component attached to it, but I can't figure out what that is. And the force would just be the 2.4 x 10^-13, because if you take the x and y components and find the magnitude it's the same thing, right? So I'm just confused... because I can't get the right answer and I'm on my last attempt.

hutchphd
Science Advisor
Homework Helper
The net force on the proton (which you are given) is the vector sum of the electric force (whose direction you know) and the magnetic force (whose magnitude and direction you know). Make a good drawing with these three forces and it should become clear how to solve this. There is more than enough info. supplied in the problem.

And the force would just be the 2.4 x 10^-13, because if you take the x and y components and find the magnitude it's the same thing, right?
Sorry I have no idea what this says. There are many correct ways to represent any vector. I think you only need the "vertical"(or y) components to get your answer, but your problem statement is a bit sketchy.

• blank_L14 and berkeman
electric force (whose direction you know)
I'm sorry I guess I'm really dumb, but how do I know the direction of the electric force? I'm given the net force and because I'm given v and B, I can figure out the direction of the magnetic force (right hand rule), but I guess the direction of the electric force might be where I'm lost? As many times as I read your responses I can't figure out what I'm missing! I do not have a physics brain and vectors in these contexts have always confused me a lot. I appreciate all the help!

berkeman
Mentor
but how do I know the direction of the electric force?
From the direction of the Electric field and the polarity of the charge, ##\vec{F} = q\vec{E}##

• blank_L14
berkeman
Mentor
BTW, it helps in posting if you learn to use LaTeX math symbols (it's pretty easy to learn). See the LaTeX Guide link at the lower left of the Edit window. You can also "Reply" to my post above to see the in-line LaTeX that I used to post that equation. gneill
Mentor
It's always good to start with a diagram.

Start with a sketch of the vectors of the known net force and the known (with your knowledge of the Lorentz force) magnetic force on the particle. Can you show this?

Then you'll need to find a force vector that when summed with the magnetic force vector results in the net force vector. That force is supplied by the electric field.

I've done the sketch myself, and to me it looks like you'll need to counteract a bit of Y-direction force and supplement a bit of negative X-direction force... Once you have those E-field force components you should be able to sketch in the E-field force vector. With that you should be able to find the field magnitude and direction.

• blank_L14
I figured it out thank you!

• berkeman