Waves and Oscillations PHYS-0232 UG Sem2 2015 Instructor : Suchetana Chatterjee Lecture 4 Electromagnetic Waves

The speed of electromagnetic radiation in vacuum is 3x1010cm/s Dimension of wavelength = [L] Frequency = How many wavelengths repeat in a second ? Dimension of Frequency = [T-1] Wavelength (l) X Frequency (n) = Speed (v) The speed of electromagnetic radiation in vacuum is 3x1010cm/s Wavelength (l) X Frequency (n) = constant higher the wavelength, lower the frequency Energy of electromagnetic radiation = hn Planck’s Law. h= Planck Constant = 6.62x10-27 units. Find out the dimension of Planck constant

The Kelvin Scale of temperature Anything that emits EM waves has a characteristic temperature. higher the temperature , higher is the energy of radiation. E= KBT KB is called the Boltzman Constant. Find its dimension.

The Electromagnetic Spectrum microwaves: mm wavelength; Find out the frequency of microwaves.

What wavelength is emitted from the SRK’s body? 97-98 degree F is the temperature. Convert it into Kelvin. ~ 309 K. To get energy we need to multiply it by the Boltzman constant. KB= 1.38x10-16 ergs/K Hundreds of Kelvin corresponds to infrared radiation. So for our purpose, SRK is roughly a black body or a thermal bath of infrared radiation.

Water Molecule Some Molecules like water have equal amounts of positive charge and negative charge, but the distribution of charge is uneven. Excess positive charge concentrated on one side and excess negative charge concentrated on the other side. This acts like an electric dipole.

Electric Dipole An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d Due to the nature of chemical bonds and the structure of water molecule the charge gets displaced and we have a dipolar distribution of charge. Water is a good solvent because of that. Salt dissolves in water. If water molecules were not electric dipoles it would be a poor solvent. All of Chemistry that occurs in aqueous solutions would be impossible. That includes all of the biochemical reactions that occur in all of life on earth. Our existence as a living being depends on electric dipoles!!!!

E is the external electric field. It is a constant Electric field. The net force is qE-qE= 0 However there is a net torque which is responsible for rotating the dipole Torque is the rotational analog of force. Torque, is the tendency of a force to rotate an object about an axis. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. We define something called the electric dipole moment p=qd The torque always tends line up the dipole moment with the direction of the external electric field. Note that: If the external electric field is not uniform there will be net force.

Electromagnetic radiation can be described by oscillating electric and magnetic fields If there is an external electric field the dipole tries to align itself with the direction of the electric field. Now we have an oscillating electric field. So the polar molecule constantly tries to align itself constantly with the electric field. This is called dipole rotation. In the process the molecules push pull and collide with other molecules redistributing energy in the form of heat. So by applying electromagnetic radiation one can cause dipolar rotation and EM waves

Electromagnetic waves in a medium Electromagnetic waves can travel through matter and its speed is less than the speed it has in vacuum. v= c/n, where n is called the refractive index of the material. EM waves can be reflected from the surface of a conductor (e.g., metal) or an insulator (e.g., glass). Also they can create standing waves. Standing waves are created in a cavity (e.g., A microwave oven)

Electromagnetic radiation is incident on the surface of a material. Part of it is reflected from the surface and the rest will be transmitted into the material. This transmitted electromagnetic field interacts with the atoms and electrons inside the material. Depending on the material, the electromagnetic field might travel very far into the material, or may die out very quickly. Penetration Depth Penetration depth is a measure of how deep any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to about 37% of its original value at the surface. For a given material, penetration depth will generally be a function of wavelength.

Problems A carbon dioxide laser emits a sinusoidal electromagnetic wave that travels in vacuum in the negative x direction. The wavelength is 10.6 micro-meter and the E field is parallel to the z-axis, with E_max = 1.5 MV/m. Write vector equations for E and B field. If E_max is 100 V/m=100N/c, find the value of B, the energy density u, and the magnitude of the Poynting vector. EM waves of frequency 5.09X1014 Hz passes through a material of refractive index 2.41. Find out the wavelengths of this wave in vacuum and within the material.