Gauss' law for concentric circles

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And I appreciate your effort to pick up some TeX know-how!

You only taught me some.

 

[gracy]

I want to sum up this long thread in a post so that if someone visits this thread he/she would not have to face problems in keeping track
My OP contained two questions.These two question had been answered in post#7 and #4 respectively

1)why charge +4q is distributed /splitted in such a manner i.e +2q &+2q and then why one +2q is put in the circle of inner radius c and one +2q is placed in the circle of inner radius of d.

Such charge redistribution for the larger sphere is required to satisfy the requirement that the electric field inside a conductor must be zero. In order to have E=0E=0 for c<r<dc

2)what is the difference between the positions p3 and p4 because my textbook states at P3 electric field would have some magnitude but at P4 electric field would be zero because it lies inside the conductor then why P3 is not considered to be inside the conductor?

the two points are at different locations. The electric field at P3P3 is due to the opposing charges on the inside of the outer conductor and outside of the inner conductor. There must be an electric field at P3P3 as a result, whereas at P4P4 the electric field should be zero because you are on the conductor itself. P3P3 is not inside a conductor because it is outside the inner conductor which has a charge on its surface and P3P3 is inside the outer conductor which also has a charge on its inner surface.

Then as the problem progressed I included a graph in post #19
Electric field changes at the surface of a conductor .Just inside the conductor it is $\frac{σ}{ε0}$.In fact,the field gradually decreases from $\frac{σ}{ε0}$ to zero in a small thickness of about 4 to 5 atomic layers at the surface.
That's why graph shows two values of electric field at surfaces i.e at r=b,r=d ,r=c
Then I faced difficulty to comprehend why the value of electric field at r=c is negative as sigma is positive 2q?And it should nullify -2q and net charg enclosed should be zero.
I was wrong to think that gaussian surface at r=c includes /contains charge +2q .
Because charge enclosed by gaussian surface for r=c is -2q,.Because we are moving outward from the center of the sphere, and at r=c, we are yet to enclose the charge on the inner surface at r=c.
As+2q is not enclosed by it it is not going to nullify or cancel -2q .Hence net charge enclosed would not be zero rather -2q.

That's it!Thanks @ehild,@blue_leaf77 @Doc Al ,@BvU ,@Zondrina @haruspex for being patient and for giving helpful answers.You guys are amazing!