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1. The problem statement, all variables and given/known data

The electric field of a uniform charged disk at a point on its axis at a distance x from the disk is given by

[tex]E = 2k_e\pi\sigma(1-\frac{x}{\sqrt{x^2+R^2}})[/tex]

where R the radius of the disk and [tex]\sigma[/tex] the surface charge density.

In my notes it says that when [tex]x\gg R[/tex], that is when the distance x to the disk is much bigger than the radius of the disk, then

[tex]E\approx k_e\frac{Q}{x^2}[/tex]

with the Q the total charge on the disk. How do they come to that result?

2. Relevant equations

3. The attempt at a solution

When [tex]x\gg R[/tex], then [tex]\sqrt{x^2+R^2}\approx\sqrt{x^2}=x[/tex]. But then I get that [tex]E=0[/tex], which is not obviously not correct.

I guess the approximation that [tex]\sqrt{x^2+R^2}\approx\sqrt{x^2}[/tex] is wrong. But how is the approximation then?

Thank you.

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# Homework Help: Approximation of electric field of uniform charged disk

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