# Fields

## Table of Contents

## Equations / Laws

### Coulomb's Law

where **permittivity constant of free space**

### Electric Field

where is the test charge, is the electric field at that point.

### Magnetic Field

### Lorentz Force

This is just writing the magnetic and electric in a single equation.

### Electric Flux

### Gauss's Law

for **Gaussian surfaces**, i.e. general closed surface with all surface elements
pointing outwards.

### Potential Difference as work

I.e. potential-difference is simply work used on a test-charge.

### Potential Energy

### Potential

### Ampere's Law

### Biot-Savarts

where is the vector whose magnitude is the length of the differential element of the wire in the direction of conventional current.

Thus, is tangential to the surface of the wire, perpendicular to the current-flow (following the right-hand rule).

### Dipole moment

where is the distance between charges and is the dipole axis.

### Continuous Charge Distribution

where

### Torque

### Faraday's Law

Induced *emf* in a conducting loop is given by the rate of change
of *magnetic flux* through the loop, i.e.

### Lenz's Law

The induced current has a direction s.t. the magnetic field due to this current opposes the change in the magnetic field that caused it.

### Capacitor

#### Charge stored

#### Impedence

## Definitions

### Electric dipole

Two charges of different charge separated by a fixed distance.

## Examples

### AC

Electromagnetic force is given by:

The resulting current is:

where is the phase-difference between and .

#### How-to

- Setup the differential equation for
*charge*wrt. time, using Kirchoff's Law and the fact that the potential difference across all components need to sum to the potential difference across the entire circuit. - Solve said differential equations.

#### Capacitive load circuit

Thus, "current" *across* the capacitor