E & M
Charges, magnetic fields, circuits, etc.
Electricity and Magnetism are two aspects of the single fundamental emectromagnetic force. Maxwell's equations and the Lorentz force law are the starting point to describing E&M mathematically.
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Force Laws
Coulomb's Law ${\mathbf {F}}=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}$
Where $q_{1}$ and $q_{2}$ are two point charges, $r$ is the distance between them, and $k_{e}$ is Coulomb's constant (ke = 8.99×109 N m2 C-2).
Lorentz Force ${\mathbf {F}}=q{\mathbf {E}}+q{\mathbf {v}}\times {\mathbf {B}}$
Where E is the electric field, B is the magnetic field, q is the charge and v is the velocity of the charge.
Maxwell's Equations
These equations describe how fields vary in space and time
Gauss's law $\nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}$
Gauss's law for magnetism $\nabla \cdot \mathbf {B} =0$
Maxwell–Faraday equation $\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$
Ampère's circuital law $\nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)$
Where E is the electric field, B is the magnetic field, $\rho$ is charge density, J is current density, t is time, and $\mu_0$ and $\epsilon_0$ are universal constants.
Conversions
Units for the magnetic field:
1 Gauss = .0001 Tesla, or 1 Tesla = 10,000 Gauss
$\mathrm {T} ={\dfrac {\mathrm {V} \cdot {\mathrm {s} }}{\mathrm {m} ^{2}}}={\dfrac {\mathrm {N} }{\mathrm {A} {\cdot }\mathrm {m} }}={\dfrac {\mathrm {J} }{\mathrm {A} {\cdot }\mathrm {m} ^{2}}}={\dfrac {\mathrm {H} {\cdot }\mathrm {A} }{\mathrm {m} ^{2}}}={\dfrac {\mathrm {Wb} }{\mathrm {m} ^{2}}}={\dfrac {\mathrm {kg} }{\mathrm {C} {\cdot }\mathrm {s} }}={\dfrac {\mathrm {N} {\cdot }\mathrm {s} }{\mathrm {C} {\cdot }\mathrm {m} }}={\dfrac {\mathrm {kg} }{\mathrm {A} {\cdot }\mathrm {s} ^{2}}}$
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