00:01
So according to this problem there are four infinite meaning very long very long wires in parallel that they are in a configuration in a square configuration yeah of site l is distance here is l and this distance here is l okay from the from the sketch here we understand let's explain these symbols.
00:35
So this indicates that the current here goes into the page, into the same with this one, into.
00:48
This is out of the page, and this is out of the page of the page.
00:55
And we have three tasks to do.
01:01
And yeah and i've got to mention that they all have the same current i okay we have three tasks to do first of all we need to determine we need to determine the magnetic field at point at p so we need to first of all using the right handle we need to find out the direction of the of the magnetic field due to each of the four wires.
01:38
And remember the magnetic field is a solenoid field.
01:41
The direction of the magnetic field.
01:43
A certain point is the tangent of the magnetic lines.
01:47
Okay.
01:48
And then the exact direction can be indicated, again, from the right -hand rule.
01:55
There are quite a few versions of the right -hand rule.
01:59
For this one, i will say just use the one.
02:02
And that the thumb indicates the direction of the right -hand rule.
02:04
The current and the curling of the hands excuse me of the fingers of the fingers i go with the direction of the magnetic lines okay therefore let's let's write down here this is the point of interest and then let's begin with this one this is the current goes out of the page so i hope that is clear that the contribution the magnetic field created by this current goes up and to the right this wire goes again the current here goes again out of the page therefore remember always go with the tangent therefore direction of the magnetic field be up and to the left this goes into the page into the page therefore direction the magnetic field will be again here up and to the left and also this one goes into the page to the page therefore it goes to the right and up therefore in total the magnetic field here should be going up the direction of the magnet at p because again yeah it's the same current therefore yeah since we have the same distance same distance okay and actually let me immediately write down the the formula for the magnetic field excuse me the magnitude of the magnetic field due to an infinitely long wire is new knot over four pi times yeah two times the current over the distance and again if the distance point p has exactly the same distance from all four wires therefore the magnetic the magnitude of the magnetic of the individual contribution to the magnetic field from each of the current is exactly the same it's just that they have different direction okay therefore necessarily the direction of b net at p yeah, up as we see on this page here.
04:38
Okay.
04:40
Next, we need the magnitude of the magnetic field at point p.
04:47
Okay, we've written down the magnetic field, the magnitude of the magnetic field.
04:56
Yeah, for a single wire.
05:01
Okay.
05:02
Now, we see that...
05:06
That this wire and this wire they contribute a magnetic field with the same direction.
05:18
While this one and this one, similarly, their contributions to the magnetic field have the same direction.
05:27
Okay.
05:31
And let me repeat one more time that the direction of the magnetic field is the tangent, tangent to the magnetic field.
05:40
Lines, therefore, yeah, from this point up to this point, tangent therefore, yeah, the line connecting the wire and the observation point and direction of the magnetic field, they have a 90 degrees angle, okay, and also yeah the same here.
06:09
So it's not difficult to see.
06:11
That the angle between the two contributions is 90 degrees therefore it's not too it's not too it's quite easy to calculate they need magnetic field okay again in apologies and before we move on let's calculate the distance here what is the distance here if we're talking about a square of sight l therefore i hope it is clear that the diagonal is just diagonal of the square is just l times square root of 2 therefore the distance of the point p to any of the wires is just l over square of 2 meaning l over square root of 2 okay, and also, let me lay it this way.
07:37
Therefore now we have individual contributions, individual contributions be wire individually, which is, yeah, from here, new or not over four pi times i over l squared of 2 so, new nod for pi 2, square root of 2 i over l.
08:17
Okay, again this is the magnitude of each of the contributions.
08:23
Now, we see that we have two contributions here and two contributions are there...