4.2.1 Sources and fields
Before we introduce the magnetic field B, recall what we learnt about the electric field E. The interaction between two charges happens in two stages. The charge Q, the source of the field, produces an electric field E around it. A second charge q placed in this field feels a force F = qE.
Like the electric field, the magnetic field has a source: moving charges, or currents. It also obeys the principle of superposition, so the field of several sources is the vector sum of the field of each one.
4.2.2 Magnetic Field, Lorentz force
Let us suppose that there is a point charge q moving with velocity v and located at position r, in the presence of both an electric field E and a magnetic field B. The force on this charge is the sum of an electric part and a magnetic part.
The magnetic force on a moving charge is always normal to both the velocity and the magnetic field, so it can turn the charge but never change its speed.Ask AI about this This has two immediate consequences. A charge at rest feels no magnetic force at all, and a magnetic field does no work on a moving charge.
The unit of magnetic field follows from the same expression. If a charge of one coulomb moving at one metre per second normal to the field feels a force of one newton, the field is one tesla.
We can now see why a magnetic field bends the path of a charged particle without speeding it up or slowing it down, which leads directly to the circular motion studied in the next section.