Question

How are frequency and energy in electromagnetic waves are related?

Answer 1

Hint: Electromagnetic waves are a form of energy propagation which is produced by accelerating charges which have both particle and wave like properties and they travel with speed of light. Electromagnetic waves carry energy from one point to another .The energy associated with EM radiation is proportional to frequency and inversely proportional to wavelength.

Complete answer:
Maxwell’ s equation showed the relationship between electric and magnetic fields and the relationship of electric and magnetic fields to the charge and current. Maxwell theory showed that accelerated charges produce electromagnetic waves. His theory predicts that electromagnetic waves always travel in vacuum with a speed of light and when vacuum is there then its speed will change.
Electromagnetic waves are produced by accelerating charges, when any oscillating body produces a wave; the frequency of that wave is the frequency of the oscillating body. Hence when oscillating charges produce an electromagnetic wave, then the frequency of that electromagnetic wave is the frequency of oscillating charge.
Let us assume frequency of oscillating charge is $$f_{Oscillating\mathrm{\_}Ch\arg e}$$
so,$$f_{e.m.\mathrm{\_}wave}=f_{Oscillating\mathrm{\_}Ch\arg e}$$
Energy of electromagnetic waves is confined in the form of electric and magnetic fields. Energy per unit volume in an electric field is given by $$u_E={\displaystyle \frac{1}{2}}{\epsilon }_0{E}^2$$.Similarly energy per unit volume in a magnetic field is given by$$u_B={\displaystyle \frac{B^2}{2{\mu }_0}}$$. Hence electromagnetic waves transfer energy to objects placed in their path. Because Electric field and magnetic field vary with time for an electromagnetic wave, the energy densities also vary with time.
By substituting $$B={\displaystyle \frac{E}{c}}$$ in the values of energy per unit volume. We get, $$u_E=u_B$$.
Energy and frequency of electromagnetic waves is related by relation$$E=hf$$.
Where,
E - Represents Energy of electromagnetic waves.
h- Represents Planck’s constant
f- Represents frequency of electromagnetic wave
We can also write expressions of energy as$$E=hf={\displaystyle \frac{hc}{\lambda }}$$.
Where $$\lambda$$ represents the wavelength of electromagnetic waves.
Energy is directly proportional to frequency of electromagnetic wave and wavelength of electromagnetic waves is inversely proportional to its energy.

Note:
Electromagnetic waves do not require any medium for propagation, so no particles of medium are available for taking energy from one point to other point .So electric field vectors and magnetic field vectors are oscillating in that case for taking energy from one point to other point.