# Electric and Magnetic field

1. May 2, 2015

Will a static electron be influenced by a magnetic field.

2. May 2, 2015

### Staff: Mentor

What do you mean by static electron?

Do you mean a stationary electron relative to a static magnetic field like an ordinary magnet?

The force on the electron is: F = qv x B where q is the charge of the electron and v is its velocity and B is the magnetic field vector.

So ask yourself what is the force on the electron if it's not moving and that should answer your question.

3. May 2, 2015

### vanhees71

Well, if there's only a magnetic field in the restframe of the electron, there'll be no force on the electron (see the previous posting). But if the magnetic field is time-dependent there's also an electric field due to Faraday's Law,
$$\frac{1}{c} \partial_t \vec{B}+\vec{\nabla} \times \vec{E}=0.$$
Then, of course the force on the electron is the full Lorentz force,
$$\vec{F}=q \left (\vec{E}+\frac{\vec{v}}{c} \times \vec{B} \right ).$$
So then it will be affected. You have to always look at both the electric and the magnetic field. In fact, electric and magnetic fields are just a split of the one and only electromagnetic field into components with respect to an arbitrary inertial reference frame.

NB: I always use Heaviside-Lorentz units, because they are the most natural ones for electromagnetism.

4. May 2, 2015

### tech99

May we say, therefore, that the electrons in a receiving antenna move only in response to the E-field of a passing wave?

5. May 2, 2015

### vanhees71

No, because when the electron moves, there's also a force due to the magnetic field, as written above.

6. May 6, 2015

7. May 6, 2015

### vanhees71

The charge produces of course a field, and in principle you have to take it into account. This is the socalled "radiation reaction" and is a tremendously difficult problem, which has not a full resolution for a point partice within classical electrodynamics. Have a look at the usual textbooks (Landau Lifshitz vol. II, Jackson etc.).