# Electric / Magnetic Field?

#### Hyperreality

Okay, I know the difference between an electric field and a Magnetic field:
An electric field can created by a presence of a charged particle such as elctron or proton. While a magnetic field is created due the relative motion of a charged particle with respect to a stationary observer, which radiates at right angle to the motion of the charged particle.

But apart from the difference mentioned above, are there any other different properties which we can use to distinguish an electric field from a magnetic field?

For example, suppose we have an unknown force field, and we insert an electron into the force field, can we determine whether the force field as an elctric field or a magnetic field by observing the trajectory of the electron in the force field?

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#### chroot

Staff Emeritus
Gold Member
Test charges in an arbitrary superposition of electric and magnetic fields feel forces described by the Lorentz force law:

F = q (E + v x B) where E and B are the electric and magnetic fields, v is the velocity vector of the charge, and q is the charge. 'x' connotes the vector cross product.

As you can see, magnetic forces always act at right angles to the velocity. As a result, magnetic fields never slow particles down -- they just bend them around in circles.

So the answer to your question is an enthusiastic "yes!" -- you can watch the trajectory of a particle and determine whether the field was electric or magnetic simply by seeing if the particle slowed down at all.

- Warren

#### JAL

Ok, I get this. Thx Chroot.

Now the EField changes the speed of the particle radially from it, it accelerates the particle. The MField changes the direction of the particle 'tangentialy', it accelerates it too. You see where I'm going don't you? Both types of fields correspond to both type of accelerations! Now there must be some deeper connections to this right ???

#### Tyger

Originally posted by JAL
Ok, I get this. Thx Chroot.

Now the EField changes the speed of the particle radially from it, it accelerates the particle. The MField changes the direction of the particle 'tangentialy', it accelerates it too. You see where I'm going don't you? Both types of fields correspond to both type of accelerations! Now there must be some deeper connections to this right ???
Boy, you catch on fast! Yes, there is a deeper connection, the electric and magnetic fields can be expressed as the electromagnetic field tensor, a single expression which contains all the information about the field at every point in space and time.

#### Creator

Originally posted by JAL
....
You see where I'm going don't you? Both types of fields correspond to both type of accelerations! Now there must be some deeper connections to this right ???
You bet there's a deeper connection, JAL. Faraday's law says that a time rate of change in a magnetic field produces an electric field.
In terms of Maxwell's eqns.:

[inte]E*dl = dB/dt Where B is the flux of the magnetic field.

Thus an electromotive force developes as a result of a changing magnetic field.

Creator

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#### jeff

It's worth pointing out that as far as we know, there are no magnetic analogues of electrically charged particles, and this is reflected in maxwell's equations by it's characterization of the magnetic field as being divergence free.

However, grand unified theories do predict the existence of magnetic monopoles, but in number densities so small that it's unlikely we'd ever see one.

Nonetheless, we can construct theories with magnetic sources that are related to the conventional ones having electrical sources by a special class of symmetry which is known as weak/strong duality since it relates one theory at strong coupling to the other at weak coupling.

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