# B A charged particle entering a magnetic field at an angle -- is work done?

1. Sep 20, 2016

### big_bounce

Hello PF's members

I know a magnetic field doesn't work on charged particles if magnetic field being perpendicular to the velocity of the particles. also i know magnetic field doesn't work if a charged particle enters with right angle into the field.

But suppose that a charged particle like electron is entering with angel 35 degree at a uniform magnetic field.
Does magnetic field work on charged particle after entering and electron gains energy? what about when magnetic field is non-uniform?

2. Sep 20, 2016

### vanhees71

A purely magnetic field never does work on the charged particle since the force is always perpendicular to the velocity,
$$\vec{F}_{\text{mag}}=\frac{q}{c} \vec{v} \times \vec{B} \; \Rightarrow \; P=\vec{v} \cdot \vec{F}=0.$$

3. Sep 20, 2016

### big_bounce

EVEN If the electron enters the field at an angle to the field direction, magnetic force remains perpendicular to the velocity?

4. Sep 20, 2016

### Staff: Mentor

Yes, the force is always perpendicular to both the field and the velocity.

5. Sep 20, 2016

### big_bounce

therefore for changing motion of object in direction we always don't have to expend (or gain) energy?

6. Sep 20, 2016

### Tallus Bryne

Think of a simple case of centripetal motion at some constant potential energy state (perhaps a "car" going around a circular, horizontal track at constant speed). The centripetal force is responsible for the change in motion, but that doesn't mean the energy changes (constant speed means constant kinetic energy).