Griffith Electrodynamics: Brief Ideas | Constants, Units, Force, Energy, Momentum | Lecture-1

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[00:00:03]So first of all we will discuss about the electronamics constants.

[00:00:21]For example, epsylon kn mu not c m e etc. Next we will discuss about electronamics units and here we'll discuss both SI system and Gaussian system.

[00:01:14]Next we'll discuss about the fundamental equations related to force, energy and momentum.

[00:01:55]Next.

[00:01:57]We'll discuss about the four different Maxial equations in general form.

[00:02:26]Now coming to the constants that is the electronamics constants and the first constant is epsylon kn that is equal to 8.

[00:02:49]85 into 10 ^ -12 kum² by Newton m²ared and this is known as the permitivity of free space.

[00:03:18]Next constant that is mu not that is equal to 4<unk>i into 10 ^ - 7 Newton by m² and this is known as the permeability of free Yes.

[00:03:55]Next C that is equal to 3 into 10 ^ 8 m/s that is the speed of light.

[00:04:15]Next m is equal to 911 into 10 ^ - 31 kg that is the mass of an electron.

[00:04:41]Next E is equal to 1.60 into 10 ^ -9 kum that is the charge of an electron.

[00:05:09]So these are the constant we have to encounter when we'll enter to the topic.

[00:05:17]Now coming to electronamics unit.

[00:05:24]Coming to electronamics unit electronamics units.

[00:05:53]And here we'll discuss the SI system as well as the Gossian system.

[00:06:08]So in SI system we have to consider kg, m and columns.

[00:06:23]That is the unit of charge.

[00:06:27]And in case of Gaussian system we have to consider, gram, cm, second and ESU that is the eloptoatic unit that is unit of charge.

[00:06:51]Correct. Now we'll see some physical quantity and their corresponding SI unit, GSEN unit and the factor that is how they are linked.

[00:07:07]So here I'm writing the quantity.

[00:07:14]This is in SI system, Gaussian system and the factor.

[00:07:29]The first physical quantity is charge.

[00:07:37]Any SI system we can write this is kulums in CGS system that is in gossian system we can take straight column or you can write ESU that is electrostatic unit and 1 column is equal to 3 into 10 ^ 9 state kum. So this is the factor.

[00:08:15]Coming to second quantity that is current.

[00:08:22]So current in SI system we can take a symbol is a here Q in cosian system we can take straight aere and the factor is here same 3 into 10 ^ 9.

[00:08:53]Now coming to our next physical quantity that is the electric field.

[00:09:09]Number three, electric field and the corresponding SI unit is volt per meter and the Gaussian unit is state volt per cm.

[00:09:40]And their relation is 1x3 into 10 ^ - 4. This is the factor that is 1 volt per meter is equal to 1x 3 into 10 ^ -4 straight volt per cm.

[00:10:04]Correct. Next.

[00:10:07]Magnetic field number four.

[00:10:11]Magnetic field.

[00:10:17]The SI unit is Tesla.

[00:10:22]That symbol is T. In Gossian system we can take Goss and the factor is here 10 ^ 4 that is 1 Tesla is equal to 10 ^ 4 goss.

[00:10:42]Next, next we can take the potential.

[00:10:50]Next one is the potential.

[00:10:57]Number five, potential.

[00:11:04]So the SI unit is volt capital V and gossian system it is state volt and here the factor is 1 by 300 that is 1 volt is equal to 1x 300 state volt.

[00:11:26]Okay. Now coming to the electric force coming to electric force.

[00:11:56]The electric force is given by kulums that is kulum's law that is f is equal to I am writing this is boldface letter that represent the force vector vector that is equal to 1 by 4 pi epsylon q1 q2 by r² into rcap. So this is the kulum's law in SI system.

[00:12:42]Now if you want to switch from SI system to Gaussian system we have to set epsylon KN 1 by 4 pi that is f is equal to q1 q2 by r² into rf.

[00:13:08]This is in gossian system.

[00:13:15]That means if you set epsylon 1x 4 pi then this entire constant will be absorbed by the area of charge. Correct?

[00:13:30]Now coming to magnetic field.

[00:13:41]Magnetic field.

[00:13:51]Coming to magnetic field.

[00:14:02]This magnetic field we can find by using the biote law that is B bold capital letter that represent the magnetic field vector is equal = to may not by 4 pi into I line integral dl cross rf by r².

[00:14:44]So this is magnetic field in SI system.

[00:14:50]If you want to switch from si to gossian then you have to set epsylon 4 pi.

[00:15:00]Now this thing will be eliminated and you can write b = i by c line integral d cross rf by r². This is in Gossian system.

[00:15:24]So extra C is it will come that is the speed of light.

[00:15:30]Correct?

[00:15:32]So the importance of the gossian system is that both electric field and the magnetic field have the same dimension.

[00:15:41]Okay. Now coming to electromagnetic force that is the combination of both electric field sorry electric force as well as magnetic force electromagnet magnetic force.

[00:16:15]This one is given by Lauren that is known as Lauren force.

[00:16:25]So we can write F is equal to Q into bracket E + V cross B.

[00:16:40]So here V is the velocity correct and this is in SI system.

[00:16:52]If you want to switch from SI to go then we can write F is equal to Q into bracket E + B / by C cross B. So this represent the force in Gsian system where the ratio of electric field to magnetic field have the same dimension of velocity.

[00:17:40]V correct.

[00:17:44]Okay. Now coming to the total energy expression for electromagnetic field.

[00:17:59]Total energy expression for electromagnetic field.

[00:18:30]That is we can write U is = 1 by 85 volume integral A² + B² into D to where this D to represent the volume element volume element.

[00:19:03]So this is the total energy expression for electromagnetic field in gossian system.

[00:19:16]If you want to switch from the gossian to si then you have to set epsylon 1 by 4 pi and may not 4 pi.

[00:19:32]Now u is equal to this will be 1x2 into volume integral epsylon ² + 1 by mu b² into d. So this is in SI system correct.

[00:20:03]Now coming to momentum.

[00:20:11]Momentum momentum.

[00:20:29]So we can write bold capital P that represent the moment of vector that is equal to epsylon into volume integral E cross B into D2.

[00:20:50]Okay. So these are the fundamental equations related to force, energy and momentum. So this will be more clear when we'll enter into the topic. Okay.

[00:21:05]Now coming to a maxial equation in general form.

[00:21:26]in general form.

[00:21:34]So this is the most significant achievement by Maxwell to unify the equations of electricity and magnetism.

[00:21:46]And the first equation is divergence of electric field is equal to 1 by epsylon into row. So where this represent the dell operator that is d by d x of icap plus d by d of jcap plus d by dz of kcap and this d operator including this dot this represent the divergence.

[00:22:33]This represent the divergence and where this row is the volume charge density.

[00:22:49]Next divergence of magnetic field is equal to zero. This is Maxwell second equation. Coming to Maxwell third equation that is the call of electric field is equal to minus del B by del T. So here this Dell operator including the cross this represent the call.

[00:23:28]This represent the call and this is delta V by delta T. This represent the time varying magnetic field.

[00:23:42]Time varying magnetic field.

[00:23:50]Next Maxwell fourth equation that is called of Magnetic field is equal to m into j + m epsylon del by delt.

[00:24:11]So where this G represent the current density.

[00:24:19]Current density obviously del by delta this represent the time varying electric field.

[00:24:32]Time varying electric field.

[00:24:40]So this is all about our first class.

[00:24:44]Next class we'll discuss the factor analysis. Thank you all of you.