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# Electricity & Magnetism Calculators

## 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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