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- Published: Friday, 15 October 2021 22:29
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ElectroMagnetism:
Both Electric and Magnetic fields go hand in hand. Although them seem very different from each other, one can be generated from the other. They appear as Electric or magnetic field depending on the frame of reference of the observer. We first look at Electric field and then at Magentic field.
Electric field/force:
This force is between charged particle at rest. Coulomb's Law for Electrostatic Force is exactly similar in form to Newton's Gravitational Force. It was published in 1785 by Charles Coulomb and is given by below formula
- Coulomb's Law: F=q1*q2/(4*Π*ε*R^2). It's similar to the formula for Newton's Gravitational law. Here instead of G, we replace it by other constant (1/4*Π*ε). q1 and q2 are 2 charges present, similar to masses m1 and m2 in Newton's Gravitational law.
- Electric Field is defined as field due to presence of charge q and is given as E = F/q2 = q/(4*Π*ε*R^2). Electric field is measured in V/m. ε is the permittivity of the material. It measures as to how well the material itself polarizes in response to the Electric Field. This happens due to natural tendency of outside charges to rearrange themselves so that the Field is reduced. If we put the charge Q in a vacuum, then there's nothing in vacuum to neutralize the field, so vacuum will have the lowest permittivity possible. For vacuum, permittivity is ε0 = 8.85*10^-12 F/m. Unit is F/m as ε=Q/E.1/R^2 = Cap.m/m^2=Cap/m=F/m.We take out the constant part (1/4*Π*ε) and call it the Coulomb Constant (ke) = 1/4*Π*ε0 = 9*10^9 N-m^2/C^2 where F = ke*q1*q2/R^2. Thus it can be seen that force is lot stronger than gravitational force (as ke is very large number).
- Relative Permittivity: Since everything has higher permittivity than vacuum, we talk in terms of relative permittivity εr which is the ratio of the absolute permittivity of medium to permittivity of vacuum. i.e εr= ε/ε0. A metal doesn't allow any Electric field to exist within itself, as any resultant Electric field will make electrons move (as electrons are very loosely bound), and they will keep moving until the Electric Field within the metal is no more there. So, if we put a charge surrounded by metal, metal will have no resultant Electric field, implying infinite ε. (NOTE: ε.appears in the denominator, implying higher ε.will reduce Electric field). Basically electrons will move to one end making that end -ve charged, while leaving the other end +ve charged. Thus a really big dipole is created in the metal which neutralizes the applied Electric field completely. For any material which is a perfect insulator, electrons can't freely roam whenever there's an Electric field. They are stuck in their positions bound to the nucleus. At an atomic level, the electron cloud in an atom might still get distorted. Electrons might get pushed away a little from the Electric Field creating a dipole. All such atomic dipoles will create an internal electric field in opposite direction to applied Electric field. How strong of the dipole is created is dependent on the material's ability to form such dipoles. Perfect Conductors may be thought of as an extreme case where such dipoles are created along the full length of the material, i.e electrons go on one side and nucleus goes to the opposite side. Polarizing insulators make limited length dipoles. Electrons are still held in place but just shifted a little. So, there is some net Electric field left. More the dipole electric field formed, less is the net electric field and higher is the permittivity of the material. Higher permittivity means you have to apply more charge to hold same potential difference, as some of the applied field will get neutralized. Permittivity is the capacitive ability of a material, and totally different than resistivity (see in Passive elements section). Silicon has εr=12, while SiO2 has εr=4. This means Si will have less Electric field and hence higher ability to retain charge for same Voltage than SiO2. Capacitors have materials known as dielectric with high εr so that they can hold more charge and hence more energy per unit of applied voltage.
Magnetic field/force:
This force is counterpart of Electric force. It's caused by magnetic charges instead of electric charges. The only thing unique to magnetic charges is that they always appear in pair, i.e +ve and -ve magnetic charges will appear together, and can never be separated. Usually Magnetic force or magnetic field is associated with magnets, but anything else can also behave as a magnet under right conditions. A magnet's North and South pole can be thought of as 2 magnetic charges, one at N and other at S, with opposite polarity. A moving electric charge behaves as a magnetic charge and causes magnetic field. Thus a stationary charge generates an electric field, while moving charge generates a magnetic field. However, moving is a relative term, and depends on the frame of reference of the observer. To 2 different observers in different frame of reference, the same charge can appear as moving or stationary, causing one to believe that the charge has an electric field, while to the other to believe that the charge has a magnetic field.
The equation for Magnetic field are slightly complicated, due to the fact that magnetic charges exist only in pairs. If we really had magnetic charges that could exist by themselves, then Magnetic forces would be similar to Coulomb's law. Infact, in was referred to as "Magnetic Coulombs Law".
F=qm1*qm2/(4*Π*(1/μ)*R^2). It's similar to the formula for Coulomb's law for electric charges, except that the 2 electric charges have been replaced by magnetic charges, and permittivity ε.has been replaced by 1/μ, where μ is the permeability of the medium.
Until 1800's, this theory of magnetic charges was held. All work in early 1800's believed in the theory of magnetic dipoles (i.e magnetic charges exist in pair, creating a dipole). These dipoles gave rise to electric field. But in 1820's, it was found that magnetic field is not generated due to magnetic charges, but rather due to current, which is generated by moving electrical charges. In 1825 Andre Ampere proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's mode.
Then how do magnets generate Magnetic field, since they don't have any current thru them?
Electomagnetism:
Maxwell's Equations.
Wave Equation:
Derivation of Wave equation (Electromagetic field) from Maxwell's equations:
Very good paper here: Wave Equation derivation