# What is the Lorentz force due to a single point charge?

The Biot-Savart law as applied to a single point charge is described to be:

Now we consider the following system of 2 similar charged particles:

By this definition, the B component from Biot-Savart law points in the z-direction (into or out of the page).

But then, the actual force F which is experienced by the object is said to be normal to B.

But this only puts the resultant force and acceleration experienced by the object back into the xy-plane without z-component, won't it?

So, the two objects' motion will stay in the same xy-plane forever, without straying into the z-component. Is this the right interpretation for the magnetic effect?

• Your question seems to be less about the Biot-Savart law and more about the force experienced by the second charged particle, that is known as the Lorentz force, $\vec{F}=q\vec{v}\times\vec{B}$, which dictates the direction the magnetic force takes on a charged particle due to some external field. Oct 25 '21 at 14:56
• why do you think the force is not perpendicular to B? In what direction do you think it is? axb is always perpendicular to a and b.
– user65081
Oct 25 '21 at 20:29
• Yes, the motion will be limited to the xy plane
– user65081
Oct 25 '21 at 20:34
• Yes. Remember the definition of cross product. It always result in a vector perpendicular to the two ones that are being multiplied.
– user65081
Oct 25 '21 at 21:11
• But you are talking of two different v's here, one is the velocity of the source charge that creates it, the other the velocity of the charge that feels it. Regarding your question, this might help physics.stackexchange.com/questions/166318/…
– user65081
Oct 25 '21 at 21:41