# Group of partcles in a magnetic field

1. May 22, 2012

### TheWire247

1. The problem statement, all variables and given/known data

A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.60 km/s in the + x-direction experiences a force of 2.10×10−16 N in the + y-direction, and an electron moving at 4.30 km/s in the - z-direction experiences a force of 8.50×10−16 N in the +y-direction.

A) What is the magnitude of the magnetic field?

B) What is the direction of the magnetic field? (in the xz-plane) (from the -ve z direction)

C) What is the magnitude of the magnetic force on an electron moving in the - y-direction at 3.40 km/s?

D) What is the direction of this the magnetic force? (in the xz-plane) (from the -ve x direction)

2. Relevant equations

F=qvxB

3. The attempt at a solution

I tried using the above formula to no success

2. May 22, 2012

### gabbagabbahey

You tried; okay, can you show us your attempt?

3. May 23, 2012

### TheWire247

F=qvxB

F/q=vxB

F/q=1600i x B

F/q=-1600j + 1600k

(2.1x10-16/1.6*10-19)/1600 = B

Then used Pythagoras to calculate the magnitude of B

4. May 23, 2012

### gabbagabbahey

Where does this 2nd equation come from? You don't know what $\mathbf{B}$ is; that's what you're supposed to calculate.

What you do know is that $$\mathbf{F}=q_{\text{proton}}(1600\text{km/s})\mathbf{i}\times \mathbf{B}=(-2.1\times 10^{-16}\text{N})\mathbf{j}$$ as well as a similar equation for the force that the electron experiences.

I'd suggest that you let $\mathbf{B}=B_x\mathbf{i}+B_y\mathbf{j}+B_z\mathbf{k}$ and carry out the cross product in both your equations and compare terms to solve for the components of $\mathbf{B}$