Notebook

# Electromagnetic Fields

## Introduction: Charge, Voltage and Current

Electromagnetic fields (EMF) are a combination of electric and magnetic force fields. They are generated through the use of electricity. Power lines, microwave ovens, TV and Radio broadcasting all generate EMF. EMF can be harmful to humans at high frequencies. However this book will not focus on risk assesment but rather on what EMF are, how they occur and how they can be analysed. In the following chapters basic understanding of vectors, derivatives and integrals is assumed.

### Important Definitions

Charge is the property of matter to exhibit a force of attraction to or repulsion from other matter. It is measured in Coloumbs. The charge also has a magnitude. The positive charge of a proton is denoted as $e$, while the negative charge of the electron is denoted as $-e$ or $q_e$.

Work is the product of the force experience by an object and the displacement that this force causes. It is measured in Joules=Newtons.metres

Voltage is the work done per unit of charge, $V=W/q$. It is measured in Volt = Joule/Coloumb.

Current is the flow of charges = the number of charges, $n.q$, that go through a surface area, $A$, with drift velocity, $v_d$, $I=n.A.q.v_d$. In other words, the current is the rate at which charge flows through a surface. The formula can be generalized to $I=\cfrac{dQ}{dt}$. It is measured in Ampere=Coloumbs/second. By convention, the current is in the direction in which the positive charges are moving and therefore opposite to electron flow.

Power is defined as $P=V.I=(W/q).(dQ/dt)=(W/dt)$, or in other words - work done per unit of time. It is measured in Watts.

Electric Current Density is the current that flows through a given surface in a certain direction, $\vec{J}=I/A$, measured in $A/m^2$. The current densities in a wire can vary, therefore the current can also be represented by summing up all the current densities accross an area, $I=\int_s \vec{J} d\vec{S}$

### Kirchoff's Current Law

Assuming there is no charge accumulation, whatever charge enters a closed surface S, leaves it. This is an example of the continuity equation and can be shown as $\oint_s \vec{J} d\vec{S} = 0$