State Maxwell's electromagnetic equations in a medium containing charges and currents.

Name: Problem 113, Chapter 5: Principles of Engineering Physics 1
Uploaded: 2021-11-02T08:09:50-08:00
Duration: 6 min 57 s
Channel: Mahnoor Amin
Description: State Maxwell's electromagnetic equations in a medium containing charges and currents.

State Maxwell's electromagnetic equations in a medium...

Key Concepts

Ampere-Maxwell Law

This law extends Ampere's circuital law by incorporating the displacement current, which accounts for time-varying electric fields. It relates the magnetic field circulation around a closed loop to both the conduction current and the displacement current through the loop, ensuring a consistent description of how magnetic fields are generated in media containing currents and time-dependent electric fields.

Faraday's Law of Electromagnetic Induction

This law describes how a changing magnetic field can induce an electric field. It explains the generation of electromotive force (EMF) in a circuit due to time-varying magnetic flux, underpinning the operation of devices like transformers and generators in various media.

Gauss's Law for Electricity

This principle states that the flux of the electric displacement field (D) emanating from a closed surface is equal to the free charge enclosed within that surface. It is essential for understanding how charges produce an electric field in a medium, where the material's permittivity plays a critical role.

Maxwell's Equations

These equations form the fundamental basis of classical electromagnetism, linking electric and magnetic fields with their sources—charge and current. They provide a complete framework to describe how electromagnetic fields propagate and interact with matter in various media.

Gauss's Law for Magnetism

This law asserts that there are no magnetic monopoles by stating that the net magnetic flux through any closed surface is zero. This means that magnetic field lines are continuous loops, a concept that remains valid even in materials and media with complex magnetic properties.

Transcript

00:01 So in this problem, we imagine a world with magnetic point charges or magnetic monopoles, magnetic monopoles, and the currents are made of these magnetic monopoles.

00:53 Now if we assume that there are nominatic monopoles, the maxwell equations are till dot e is equal to row over permittivity of free space, till cross b is equal to 0, till cross e is equal to negative t v by d t and del cross p is equal to mu not time primitivity of e space times d e divided by d t plus mu not j now if we denote the electric current as je and electric charge density as row e and the magnetic magnetic charge density as rho m and magnetic current as jm.

02:23 So we expect the second equation of the maxwell to change since it is an expression for the fact that there are no magnetic field sources as to oppose the electric.

02:46 Charge.

02:47 So the equation will be replaced by del.

02:51 Dot b is equal to a times row m, where a is an unknown constant and it depends on the unit of the magnetic charge.

03:04 Now this third equation should also change to resemble the fourth equation, that is, this third equation should also change to resemble this fourth equation.

03:18 So this third equation should change to resemble the fourth equation, that is to accommodate the fact that the magnetic current exists.

03:26 So similarly to the electric current, a magnetic current is created by the magnetic charge and movement.

03:34 So we can therefore define the magnetic current as jm is equal to row m times v.

03:52 So the third maximum equation will then become del cross e is equal to negative del b by del t plus b times the magnetic current.

04:11 Now this b again is an undetermined constant.

04:18 Now what will we do next? now we have to connect this a with b.

04:27 So there is a way to connect this a with b by using the continuity equation that is dell .jm is equal to negative rho m divided by dt...

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