Definition 27.6.1. Lorentz Force.
The Lorentz Force is defined as the sum of the electric and magnetic forces on a charge
\begin{equation*}
\vec{F} = q\vec{E} + q\vec{v}\times\vec{B}
\end{equation*}
Section 27.6 The Lorentz Force
Based on what you discovered in the previous section, you can define the force that a magnetic field exerts on a moving charge to be
\begin{equation*}
\vec{F}^B = q\vec{v}\times\vec{B}
\end{equation*}
where \(\vec{B}\) is the magnetic field, \(q\) is the charge experiencing the force, and \(\vec{v}\) is the velocity of the charge experiencing the force. When added to the force on a charge by an electric force, you arrive at the full expression for force in electromagnetism, which is known as the Lorentz Force.
Subsubsection Activities
Activity 27.6.1. Magnetic Force from a Wire.
In Magnetic Field of a Wire, you determined the magnetic field due to a long, straight current. Assume a small positive charge is currently located at each of the four marked points, moving downward with known speed \(v\text{.}\)
(a)
For each point, draw a vector representing the magnetic force on the moving charge.
(b)
Determine the magnitude of the force in each case.
(c)
How would your answers change if the charges were moving to the right?
(d)
How would your answers change if the moving charges were negative?
