electric field of a charged disc on an axial point.
I need to find the electric field of a uniformly charged disc at a point on its axis through the centre. At first I calculated the potential Φ.
Φ=(σ/2ε0)[( a^2 + x^2)^(1/2)  x ] where a is the radius of disc, x the distance of axial point from centre of the disc and σ the charge density.
I am following nayfeh and brussels pg 53 54 along with purcell berkley physics 5556 and university physics young zemansky 12th ed pg 732 example 21.12.So far the books are not conflicting with the answer.
Now to find the electric field I am using the following formula E =  dΦ/dx (x^)
Now x=(x^2)^(1/2).So dx/dx=x/x
And d( a^2 + x^2)^(1/2) /dx= x( a^2 + x^2)^(1/2)
So E=(σ/2ε0)[x/x  x( a^2 + x^2)^(1/2)](x^) inserting ve.
Now if x> 0 then E=(σ/2ε0)[1  x ( a^2 + x^2)^(1/2)](x^)
As x/x=1.x=+x
This is also consistent with the books.
If x <0 E=(σ/2ε0)[1  x( a^2 + x^2)^(1/2)](x^)
As x/x=1.x=x
This is what I am getting.But in nayfeh the following answer is given for x<0. E=(σ/2ε0)[1 + x( a^2 + x^2)^(1/2)](x^).How is the term x( a^2 + x^2)^(1/2) be positive??
Also if I substitute random arbitrary values to a and x say a=5units x= 10 units then for x> 0 E=0.106σ/2ε0(x^).By principle at an equal distance at the back of the disc E=0.106σ/2ε0(x^).
But if were to consider nayfeh then E=1.89σ/2ε0(x^).So who is right?? Did I do something wrong ?
