Is the Lorentz force applied to bulk objects?

Question

Assume that a bulk uniformly charged ($+Q$) nonconductive sphere is set in motion inside a uniform magnetic field. Is it correct to claim that the trajectory of the bulk sphere inside the magnetic field is the same as that for a point charge of $+Q$? What if we use a bulk conductive sphere instead? In this case, does the Lorentz force upset the uniform distribution of the charges on the surface of the sphere? If so, is the trajectory similar to that of a point charge?

In addition, I want to know if there are experiments in which the Lorentz force is exerted on bulk objects rather than the sole electrons or protons.

Answer 1

1.You have the same force on any point charge in your object, so the sphere would start to rotate and also go in the direction of the Lorentz force. in the conducting sphere you would have the uniform would be disturbed, the charges moving in direction of the force till the electric field is as strong as the Lorentz force. In every electric generator you have a bulk object with moving charges.

Answer 2

The term "Lorentz force" refers to the formula giving external EM force on microscopic charged particles, such as electrons:

$$ \mathbf F = q \mathbf E + q\mathbf v \times \mathbf B $$ where $q$ is charge and $\mathbf v$ is velocity of the particle and $\mathbf E,\mathbf B$ are fields due to external sources (not the particles themselves).

Thus it is not supposed to apply to macroscopic bodies, at least not directly. Such bodies manifest e.g. electric polarization, and even body with zero net charge experiences electric force. For example, small pieces of paper are attracted to electrically charged objects, even though the pieces are not charged.

If one sums all the Lorentz forces on all microscopic particles that make up the body, one may obtain a formula for net EM force on macroscopic body. In general this is not trivial, because there are many particles, complicated integrals, and internal forces turn out to have non-zero contribution whenever the body accelerates. In special cases (body/medium does not move), one may express macroscopic EM force using specialized formulas in terms of fields and their gradients.

Answer 3

Each charge on the nonconducting sphere has the same velocity, so the non-conducting sphere will move the same way a point charge would, in a helical motion.

Answer 4

When electrons move through a magnetic field, four things happen: 1. the magnetic dipole of the electron aligns with the external magnetic field, inducing the emission of photons, which 3. and 4. leads to the re-deflection of the dipole and the deflection of the electron from its trajectory. This is best seen in a free-electron laser, which is also nothing other than the application of the Lorentz force, but is primarily aimed at photon production.

Now, if a non-conducting sphere with an excess charge moves through an external magnetic field, then all magnetic dipoles will be deflected in the direction of the external magnetic field, but since this happens from all possible starting positions, the total deflection of the magnetic dipoles will be zero. Furthermore, the non-conductor becomes more or less magnetic and remains in this state until it leaves the external field. A deflection of the body as a whole does not take place.

What if we use a bulk conductive sphere instead? … does the Lorentz force upset the uniform distribution of the charges on the surface of the sphere? If so, is the trajectory similar to that of a point charge?

For a conductor, a minimal deflection takes place because of the Hall effect (which is nothing other than the Lorentz force). Only if the conductor were a current-carrying conductor, with new electrons constantly crossing the magnetic field, would we have a permanent transverse force.