# Electric and Magnetic field

Will a static electron be influenced by a magnetic field.

jedishrfu
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.

vanhees71
Gold Member
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.

• muscaria
tech99
Gold Member
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.
May we say, therefore, that the electrons in a receiving antenna move only in response to the E-field of a passing wave?

vanhees71
Gold Member
No, because when the electron moves, there's also a force due to the magnetic field, as written above.

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,
$$\frac{1}{c} \partial_t \vec{B}+\vec{\nabla} \times \vec{E}=0.$$

What did you do with the charge? Doesn't it produce a field?

vanhees71
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