# Charged Particle in Magnetic Field

spoonthrower
A magnetic field has a magnitude of 1.2*10^-3 T, and an electric field has a magnitude of 5.4*10^3 N/C. Both fields point in the same direction. A positive 1.8*10^-6 C charge moves at a speed of 3.6*10^6 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge.

I know Force produced by electric field is F=qE
I know Force produced by magnetic field is F=Bqv

How do i do this problem?? thanks.

## Answers and Replies

Mentor
You need to write the vector equations for those two forces. The first equation is easy to write in vector form (not much of a change), but be sure to include the cross product when you write the second equation in vector form. Once you have the two forces expressed as vectors, just align the problem with some coordinate system (like aim E and B along the z axis and fire the particle through the origin going in the x direction or something....

spoonthrower
what is a cross product?? I dont understand. do i add the two forces together?? how do you write an equation in vector form???

MrJunkpile
spoonthrower said:
what is a cross product?? I dont understand. do i add the two forces together??

the cross product of B and v would be the product of their magnitudes and sine of the angle between them. This will result in a vector with a direction normal to both B and v (right hand rule).

Yes, essentially what you need to do is add the two forces together.

spoonthrower
i figured it out. using the right hand rule, the electric field force and the magnetic force are 90 degrees from each other, so i used the pythagorean theorom to get the answer which is what i did initially but this online HW doesnt follow the right sig fig rules....i figured out the answer a long time ago. lol.

Mentor
One other thing to keep in mind. The "net force" answer will change with time, so your calculation is only valid for the instant t=0. Charged particle motion in combined electric and magnetic fields is pretty cool. If it were just the E field, the particle gets accelerated along the line of the E field (which way depends on the whether the particle's charge is + or -). If it were just the B field, the particle orbits around the B field lines' axis -- the acceleration caused by the F = qv X B force is centripital (normal to the velocity of the particle), so the particle just goes around in a constant circle whos radius depends on the charge, velocity and B field strength.

But when you combine the B and E fields as in this problem, you get some kind of spiralling motion, and the radius of the spiral generally changes as the particle has a net acceleration from the E field.