# Acceleration of an electron due to Magnetic and Electric fields

Homework Statement:
An electron has an initial velocity of (12 j^ + 15 k^) km/sec and a constant acceleration of (2e12 m/s^2)i^ in a region in which uniform electric and magnetic fields are present. If the magnetic field is (400e-6 T)i^ find the electric field vector.
Relevant Equations:
f=ma, vectorFb= (vector v cross vector B)
I figured that we would simply add up the forces acting on the electron (the electric force Fe and the magnetic force Fb) and then equate this to the given acceleration multiplied by the mass of the electron like so.

vector Fe + vector Fb = (mass of electron) (vector acceleration)

since vector Fb = q(vector v x vector B) we have

vector Fe = (mass of electron) (vector acceleration) - q(vector v x vector B)

And, since vector Fe = (q) (vector E) we have

vector E = ( (mass of electron) (vector acceleration) - q(vector v x vector B) ) / q

Then we simply plug and chug.

However, the solutions manual is saying that the solution equation is of the form

vector E = ( (mass of electron) (vector acceleration) + q(vector v x vector B) ) / q

I cant figure out why.

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
I cant figure out why.
Please show exactly what you did when you "plugged and chugged". Maybe you made a mistake in plugging or chugging or both. Be sure you keep tack of your vectors correctly. Three equations are involved here because the acceleration and the net force are three-dimensional.