A magnetic field is a vector field that exerts a force on moving electric charges and magnetic dipoles. It is produced by electric currents, changes in electric fields, and intrinsic magnetic properties of materials.
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The direction of the magnetic field at a point is given by the direction of the north pole of a compass needle placed at that point.
Magnetic field lines never intersect and are directed from the north pole to the south pole outside a magnet.
$\text{Biot-Savart Law}$ describes how currents produce magnetic fields: $$\vec{B} = \frac{\mu_0}{4 \pi} \int \frac{I d\vec{l} \times \hat{r}}{r^2}$$
Faraday's Law of Induction states that a changing magnetic field within a loop of wire induces an electromotive force (EMF) in the wire: $$\mathcal{E} = -\frac{d \Phi_B}{dt}$$
The strength of a magnetic field is measured in Tesla (T) or Gauss (G), where $1 T = 10^4 G$.
Review Questions
What is the relationship between electric currents and magnetic fields according to Biot-Savart Law?
Explain how Faraday's Law of Induction relates to electromagnetic waves.
Describe how you would determine the direction of a magnetic field using a compass.
Related terms
Electromagnetic Wave: A wave consisting of oscillating electric and magnetic fields, which propagate through space at the speed of light.
The force exerted on a charged particle moving through both electric ($$E$$) and magnetic ($$B$$) fields: $$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$.