Workshop 7 - Source of Magnetic Fields - Moving Charges

ELEC2300s

The magnetic field ${\vec{B}}_{pointcharge}$ created by a moving point charge $q$ is described by the Biot-Savart law:

$${\vec{B}}_{pointcharge}=\frac{{\mu }_0}{4\pi }\frac{q\vec{v}\times \hat{r}}{r^2}$$

where ${\mu }_0=4\pi \times 10^{-7}$ $Tm/A$ is the permeability constant, $r$ is the distance from the charge and $\hat{r}$ is a unit vector that points from the charge to the point where we want to calculate the field.

Question 1.1 - Multiple Choice

In order to produce the same magnetic fields, positively and negatively charged particles would need to:

1. Travel in opposite directions
2. Travel in the same direction
3. Change one of their charges, otherwise it isn’t possible.

Answer: Travel in the opposite direction (1).

2 | Magnetic Field of a Current

The magnetic field of a current-carrying wire builds on the idea of the moving charge. In this context, it is useful to adapt the Biot-Sawart law to

$${\vec{B}}_{current,segment}=\frac{{\mu }_0}{4\pi }\frac{q\vec{v}\times \hat{r}}{r^2}$$

The magnetic field due to the whole wire we can calculate by using the principle of superposition, i.e. by summing up the field due to many small segments.

3 | Ampere’s Law