(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There's 3 quarters of an annulus with inner radiusaand outer radiusb. It occupies the first 3 quadrants. Its charge density is [tex]\sigma[/tex]. I must calculate the electric field at the point in the middle of the "annulus".

2. Relevant equationsNone given.

[tex]d \vec E =\frac{kdQ \vec r}{r^3}[/tex].

3. The attempt at a solution

After 2 attempts, I came up with the idea of separating the annulus in this way: the left part of it, i.e. the part of the annulus situated in the 2nd and 3rd quadrants and the right part of it, i.e. the part situated in the first quadrant.

I calculated their contributions to the electric field to be [tex]k\pi \sigma \ln \left ( \frac{b}{a} \right ) \hat i[/tex] and [tex](-\frac{\sqrt 2}{2}k\pi \sigma \ln \left ( \frac{b}{a} \right ) \hat i, -\frac{\sqrt 2}{2}k\pi \sigma \ln \left ( \frac{b}{a} \right ) \hat j)[/tex], respectively.

Adding them up, I finally reached [tex]\vec E = \left ( \left ( 1 - \frac{\sqrt 2}{2}\right ) k\pi \sigma \left ( \frac{b}{a} \right ) \hat i , -\frac{\sqrt 2}{2} k\pi \sigma \left ( \frac{b}{a} \right ) \hat j \right )[/tex].

Is my method for solving the problem good? Do you know any other way to solve it? Lastly, is my answer errorless?

I thank you in advance.

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# Homework Help: Electric field of 3 quarters of an annulus

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