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--- 184_notes:b_summary [2018/03/15 22:39] – dmcpadden
+++ 184_notes:b_summary [2020/08/23 22:22] – dmcpadden
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+/*[[184_notes:i_b_force|Previous Page: Magnetic Force on Current Carrying Wires]]
+[[184_notes:e_b_summary|Next Page: Summary of Electricity and Magnetism (thus far)]]*/
 ===== Summary of Magnetic Fields and Force =====
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 From this model, we can generate the magnetic field for a number of distributions of moving charges: [[184_notes:b_current|line currents]], [[184_notes:b_shapes|rings of current, solenoids]], and [[184_notes:perm_mag|permanent magnets]] — for which the story is a bit more complicated than the others. The magnetic field, much like the electric field, [[184_notes:superposition_b|superposes]], so we can just add up the contributions to little chunks of moving charge (chunks of current) to find the field:
-$$\vec{B} = \dfrac{mu_0}{4 \pi} \int \dfrac{I d\vec{l} \times \hat{r}}{r^2}$$
+$$\vec{B} = \dfrac{\mu_0}{4 \pi} \int \dfrac{I d\vec{l} \times \hat{r}}{r^2}$$
 This is called the Biot-Savart Law, but is really just an expression for superposition of the magnetic field. Later we will find that the pattern of the magnetic field in some cases suggests a short cut to finding the magnetic field that doesn’t involve superposition integrals.