Electromagnetism is one of the four fundamental forces of nature. The very infrastructure of modern human civilization depends upon harnessing this fundamental force and using it to generate consumable power. Naturally, the study of electromagnetism is core to almost every science & technology course.
This article offers a bunch of essential insights on electromagnetism. It comes straight from the experts of MyAssignmentHelp.com, a leading homework help service in the USA. It looks into the relationship between electricity & magnetism and the fundamental equations & concepts.
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The Heart of Electromagnetism – Maxwell’s Equations
Electromagnetism is fundamental to the natural processes of this universe. It governs the interactions and, thereby, the reactions between atoms & molecules. The force binds atoms together and determines the properties of every element & compound. Electromagnetism operates at every perceivable and unperceivable scale, generating light & power and transforming lives & society.
All aspects of non-quantum, classical electromagnetic phenomenon can be described using Maxwell’s equations. There are four governing equations, which are as follows: à
E, B, j, and ρ are functions that denote electric field strength, magnetic field strength, electric charge density, and electric current density, respectively. And each function depends on two critical, independent variables: distance & time. ε and m are the electrical permittivity and magnetic permeability, respectively. The nabla operator denotes divergence at a three-dimensional point r (x,y,z).
Divergence measures the vector flowing out of an imaginary surface surrounding a point in space. If divergence is positive, then the vector flow is out of the point of the measurement; if it is negative, the flow is inwards.
- Equation 1 is the corresponding version of Coulomb’s Law and denotes the electric field generated by a point charge.
- Equation 2 indicates that there can never be a magnetic monopole.
- Equation 3 is the equivalent of Faraday’s Law of Electromagnetic Induction and states that a changing magnetic field produces a corresponding electric field.
- Equation 4 corresponds to the Biot-Savart law and denotes the magnetic field generated by changing electric fields.
If we take the divergence of equation 4 and then combine it with equation 1, we will have à
Converting the above equation into its corresponding integral form and using the divergence theorem, we get the following expression -à
[The divergence theorem is a vector calculus theorem and states that, in the absence of the destruction of matter, the only way for the density of a bounded space to change is through the inflow or outflow of space across the boundary.]
In the above expression, if we consider it a fixed volume bounded by a surface S, the sum of the total electric charge density and the total current density over the bounded volume is zero. That is, the total charge density in the bounded volume of space is equal to the outward flux or flow of charge or current on the bounding surface. It is a statement of the universal law of conservation of energy.
Maxwell’s 3rd equation lies at the heart of electrical power generation, making it the most important among the four.
Power Generation using Electromagnetism
The third equation is the equivalent of Faraday’s law of electromagnetic induction.
It states that a changing magnetic field along a surface induces an outflowing electric field. Michael Faraday conducted a simple experiment that surrounded the opposite ends of a soft iron core with two conducting wire coils. He created a circuit with a power source with the coil on one end. He then connected the coil on the other end with a compass. There was no connection between the two wire coils on the opposite ends of the soft iron core.
When the coil circuit connected to the power source was closed, the compass connected with the other coil would rotate briefly and then stop. The same thing would happen when the circuit was opened. The compass would rotate for a very brief amount of time.
Future experiments replaced the compass and connected the powerless end of the iron core with an ammeter. The ammeter would show a positive and negative current spike in the coil when the power circuit on the other end was opened.
Faraday figured out a change in the magnetic flux in the powerless coil, which generated a corresponding electricity spike. The change in the magnetic flux was induced in the powerless coil due to a change in the electric field in the powered coil.
And therein lies the entire idea behind electrical power generation. Faraday’s version of Maxwell’s third equation is à
The magnetic flux is the change in the magnetic flux within a space that generates an electromotive force due to a change in the corresponding electric field. EMF is the electric voltage or potential that’s produced due to the changing electric field. The negative sign denotes that the induced voltage is opposite to the time-rate change of the magnetic flux.
Well, that’s all the space we have for today. I hope this was an informative read. Work hard & study well to master electromagnetism. Aim for the best grades in your assignments, & if you think of some expert aid, then contact MyAssignmentHelp.com, USA’s largest & oldest physics homework help service.
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