00:01
So here we are given the section for a long thin wallet metal tube of radius, capital r equals to 3 .00 cm.
00:11
With charge per unit length, that is, lambda is equal to 2 .00 into 10 to minus 8 cullum per meter.
00:20
So we have to find the magnitude of the electric field at a radial distance, when in the first case, small r will be equal to capital r divided by 2.
00:34
And in the second case, when a small r would be equal to the capital r into 2.
00:41
And in the third case, we have to draw the graph for e versus r for the range of r equals to 0 to 2r.
00:50
So let us start with the first part.
00:53
So first of all, let us look to the figure.
00:55
So this is nothing but what the figure.
00:57
Which we are given here according to question in which you can see that the cross -sectional of this tube is given to us whose radius is capital r which is according to question is given to us 3 .00 cm now we have to find the electric field along the radial axis which you can see here into the diagram right so first of all let us talk about the key concept which we are going to use here is the gauze law.
01:29
So according to goss law, what we know that, that is, if we are given a gaussian surface of reddish small r and unit length concentric with the metal tube, so in that case, according to the symmetry, the close loop integral of a, uh, e bar into d a bar, this is nothing but is equal to a, a, a close, okay, upon, on epsilon knot.
01:59
So from here if you see this is nothing but a pipe which will should be a cylindrical one.
02:06
So from here we can say that for this pipe two pi would become equals to q in close per epsilon not right.
02:15
So from here the electric field trot the axial axis that is e would be quashed to the q in close per per two pi epsilon not.
02:26
Now, in the the first part that is in a part, we have to calculate this electric field along the axial for the value of small r equals to capital r divided by 2.
02:39
Now see here, according to gauss law, whatever the electric field is generated there, just because of the charges enclosed by it.
02:52
And as you can see here, this small r is nothing but half of the capital, while if you see capital r is the radius for the cylindrical surface right, cylindrical pipe, right? so from here we can say that as the small r is less than to the capital r means the radius of the given surface...