00:03
Okay, so here is a question 29 .7.
00:11
We are given a long wire.
00:17
So let's see the current flows upward and we want to find magnetic field at some point here.
00:27
The best thing to do is use right hand thumb row.
00:32
So if you use right hand thumb row.
00:46
That means if this is your thumb pointing upwards, then at this point your fingers will call into the computer and here it will come out of the computer so it goes like that so at this point it goes into the page so i would write then so it would be magnetic field at r so this is a point this is a distance r would be some it goes in to the base and there is with that is the direction of the magnetic here it goes into the base it was any way to the left it would be out of the base let's compare between two points here let's think about another point here and if we compare the strength of magnetic field it would be more strong closer to the wire and the further and further you go it becomes that strong so here i would write r as inversely proportional to b larger r smaller b smaller r larger b and larger the current larger the magnetic field so i will just write i here and space if it was water if it was oil or some other things it might change so this gives the property of this space and that is 2 pi which basically means 360 degree it comes because of the symmetry.
02:42
Okay, so you might have seen this equation here.
02:47
So magnetic field at point r would be depending on the current i and the distance are asked how would happen here.
03:16
There is another electrical look this is a wire and we are asked.
03:21
We need to figure out if current passes through it.
03:24
It is given there is...
03:41
So in the second problem we are asked what is the flux that passes through this blue stripe.
03:58
So first of all let's figure out what is flocks.
04:03
Before that let's see what magnetic field intensity is.
04:07
This b basically means total flux.
04:12
In one unit area that means if this is a flux on the average of this is the flux on average area of one unit square so if you want to find a total flux we need to multiply that by area right so the flocks so the flocks on a very smooth stripe we call it d5 because this is a very small reason and just write negative fill of flux and this is basically equal to the magnetic field times area because magnetic field is total flux per unit area let's see define over here in this case i would just write d a which is also it also represents the area but since this is a very small area this is just keeping the mathematical consistency we times d a so b you can copy it from there and d a this is this length is l and if this is small length is d r then the area would be l times d r so this is the flux of this small stripe now if you go to the whole area we know that it is a from the wire and the distance this point is b from the wire that means if we then then this r is the distance right r goes from a to b r goes from a to b let's integrate them then it gives total flux of this whole look so integrating means just adding so we basically what we're doing is we're adding all this is small stripes from a to b so if we integrate then we get we are integrating our d r right so let's separate then it on that contains r d r over r and then there is mu not there is i there is two pi i'm just writing value of b b equals mu not i over 2 pi this is the direction so the r goes here and then the remaining is l and it goes integration from it to b to b let's see what i did i integrated this equation from a to b and the only the only thing that i need to is r the rest of them are kind of constant for this differential d r now if you integrate you can get mu not mu not i i l over two pi i l over 2 pi and log of v.
08:22
A over a.
08:29
So this is log r then it will be log b minus log a and that it will be log b minus log a is log b over a and this is how it will look so this is still three...