# Electromagnetic energy

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Content – Forms of energy

Electromagnetic energy is a form of energy that is reflected or emitted from objects in the form of electrical and magnetic waves. The energy carried by an electromagnetic wave is proportional to the frequency of the wave. The wavelength and frequency of the wave are connected via the speed of light.

## Waves

Any vibrating body that is connected to its environment (matter) will transfer energy to its environment. The vibrations and thereby the energy is transferred through the environment from neighbour to neighbour i.e. the wave motion. Waves transfer energy through a matter without changing the physical location of the matter

## Transverse waves

When waves transfer energy by pulling neighbours perpendicular to the direction of travel, the waves are called transverse waves.

## Electromagnetic waves

Electromagnetic waves (X-rays, light, radio and radar waves) are examples of transverse waves formed by electric and magnetic fields vibrating together at right angles to the wave’s motion. They don’t need any medium so they can move through a vacuum. They all move at the same speed of 300,000 km/sec (299792458 metres per second). when they travel through vacuum. They slow down when they travel through a medium.

Mechanically twisting or pulling a medium sideways is called shearing so waves formed this way are also called shear waves.

An electromagnetic wave has both electric and magnetic fields where the energy associated with the electric field is equal to the energy associated with the magnetic field.

There are various forms of electromagnetic energy including gamma rays, x rays, ultraviolet radiation, visible light, infrared radiation, microwaves and radio waves.

Accelerating charges creates electromagnetic waves. Moving charges back and forth produce oscillating electric and magnetic fields that travel at the speed of light.

## Speed of light

The speed of light and other electromagnetic waves, in vacuum is 299792458 metres per second a physical constant denoted; c ≈ 3,00 * 108 m/sec.

Nothing can travel faster than light in a vacuum.

The speed at which light travels through transparent materials is less than c.

The ratio between c and the speed at which light travels (v) in a material is called the refractive index (n) of the material n;

$n= \dfrac{c}{v}$.

## Example – Visible light

For visible light the refractive index of glass is n= 1.5, meaning that light travels at ;

$\dfrac{c}{1,5} \approx{200000} km/sec$

For visible light the refractive index of air is n= 1,0003, meaning that light travels at:

$\dfrac{c}{1,0003} \approx{299700} km/sec$

which is around 90 km per sec slower than c.

Electromagnetic waves carry no mass but do carry energy. It also has momentum, and can exert pressure (radiation pressure).

The energy carried by an electromagnetic wave is proportional to the frequency of the wave.

The Electromagnetic spectrum is divided based on frequency and waves are split into different categories based on their frequency or wavelength which also represents the energy of the electromagnetic waves.

High frequency and short wavelength constitutes higher energy than long wavelengths and low frequency.

Visible light ranges from violet to red with violet light having a wavelength of 400 nm, and a frequency of 7.5 x 1014 Hz and red light with a wavelength of 700 nm, and a frequency of 4.3 x 1014 Hz.

Visible light only represents a small part of the electromagnetic spectrum.

Electromagnetic waves that are of higher energy than visible light include: Ultraviolet light, X-rays, and gamma rays.

Electromagnetic waves that are of lower energy than visible light include: Infrared light, microwaves, and radio and television waves.

## Energy calculation – Electromagnetic energy

When calculating electromagnetic energy we need to introduce a physical constant denoted h , the Planck constant, which is related to the quantization of light and matter.

In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency. Atomic unit systems are based on the Planck constant. The Planck constant has dimensions of physical action; these are the same as those of angular momentum, i.e., energy multiplied by time, or momentum multiplied by distance. In SI units, the Planck constant is expressed in joule seconds (J⋅s) or (N⋅m⋅s).

The value of the Planck constant is:

h = 6,626069 * 10-34 Js (Joule second)
h = 4,135667516 * 10-15 eVs (electron Volt second)

When the frequency is expressed in terms of radians per second instead of cycles per second it is natural to use the angular frequency (angular frequency) then a factor of 2π is absorbed into the Planck constant. This is called the reduced Planck constant constant. It is equal to the Planck constant divided by 2π, and is denoted “$\hbar$

The value of the reduced Planck constant is:

$\hbar = \dfrac{h}{2\pi} 1,054571* 10^{-34} Js (Joule second)$

$\hbar = 6,58211928* 10^{-15} eVs (electron Volt second)$

A photon is an elementary particle with zero mass, a quantum (discrete bundle) of light and all other electromagnetic energy. Photons are always in motion and, in vacuum, have a constant speed of light.

## Formula – Electromagnetic energy

The energy for one individual photon is:

$E = hv = \dfrac{hc}{\lambda} (Joule)$

or if angular frequency is used:

$E = \hbar w$

ω  = 2πv
ν   = Frequency (cycles/second)
λ   = Wavelength (metres)
c   = Speed of light (metres/second)

1 Hz = 1 hertz; cycle per second (frequency)
1 nm = 10-9 m, nanometre (for wavelength of IR, visible, UV and X-rays).
1 pm = 10-12 m, picometer (for X-rays and gamma rays).

To calculate the energy giving the result in everyday quantities we need to calculate the combined energy for larger number of particles.