Finding magnetic field component

[wendo]

Homework Statement

An electron has a velocity of 1.63×104 m/s (in the positive x direction) and an acceleration of 1.98×1012 m/s2 (in the positive z direction) in uniform electric and magnetic fields. If the electric field has a magnitude of 19.8 N/C (in the positive z direction), what is the y component of the magnetic field in the region?

Homework Equations

this I'm really not sure... but could lorentz force law be applied to this question?

F=q(E+vxB)

C^2= a^2+b^2?

The Attempt at a Solution

I'm really sorry but I seem to really have no idea bout this one... here's what I thought but is wrong..

Since they give you the acceleration in the z direction, with it the force due to the movement of the electron can be found. (or does this not work because F=ma doesn't apply to electric forces?)

-then I thought maybe if I found the force then i can use Lorentz' equation to solve for B?

But because the question is asking for a y component I'm really stuck on how to relate the acceleration, velocity and E field into finding the magnetic field.

Can someone help push me towards the right direction for this question?? Thanks!

 

[Dick]

Yes, lorentz force law. And F=ma applies to all forces. If you think about F=q*vxB you will realize that with v is the x direction that an x component of the magnetic field will contribute no acceleration and a z component will contribute only to the y acceleration. So the only two things contributing to z acceleration are y component of the magnetic field and the E field. Does that help?

 

[m2003]

I would approach this problem by first understanding the principles and equations involved. The Lorentz force law is indeed applicable in this situation, as it relates the force experienced by a charged particle moving in an electric and magnetic field. However, in this case, we are not given the charge of the electron, so we cannot directly use this equation.

To solve for the y component of the magnetic field, we can use the equation F=qE, where q is the charge of the electron and E is the electric field. We can also use the equation F=ma to relate the force to the acceleration of the electron.

Next, we can use vector addition to determine the magnitude and direction of the total force acting on the electron, which is the sum of the electric and magnetic forces. This will give us the magnitude of the magnetic field component in the y direction.

Finally, we can use trigonometry and the given velocity to determine the angle of the magnetic field with respect to the x-axis. This will give us the full vector representation of the magnetic field in the region.

In summary, we can use the equations F=qE and F=ma, along with vector addition and trigonometry, to solve for the y component of the magnetic field in this scenario. It is important to fully understand the principles and equations involved in order to approach and solve the problem correctly.