Force on electron in magentic field

[kfcman289]

---

Members don't see this ad.

My EK book is saying that a magnetic field can never do work on an electron because the force is always perpendicular to the motion of the electron. But the equation mv2/r and qvbsin clearly show that there is a velocity, which means kinetic energy was gained, so work was done right?

Thanks

 

[sillyjoe]

Work is not done by the magnetic field because work is FDcos(theta) so it is impossible for the magnetic field to do work since theta is 90 degrees with the magnetic field.

However, the electric field will do work on the electron.

 

[t5Nitro]

But the equation mv2/r and qvbsin clearly show that there is a velocity,

Thanks

The magnetic force causes a centripetal acceleration in the charged particle which is why you have a velocity. If the particle is moving at constant speed but in a circular path, then there is velocity because the vector is constantly changing direction. Likewise, there is an acceleration (centripetal here) as well even though the speed is constant.

The magnetic force equation F_b = qvB can be set equal to F = ma to give qvB = ma where 'a' is your centripetal acceleration v^2/r and you get qvB = m(v^2/r).