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optimization - Find an expression for the intensity I(x) at the point P.

Please look at the attachment for the queation part a), i provided the answer which i thought is correct and it says its wrong. Can someone please tell me whats wrong with expression i provided, and how it should look.

Re: optimization - Find an expression for the intensity I(x) at the point P.

The intensity due to 1 source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. The constant of proportionality is 1, so the equation must be of the form:

$\displaystyle I=S/D^2$

Where S is the strength of the source and D is the distance. This is the intensity due to 1 source, so the intensity due to the other source is

$\displaystyle I_{2}=S/D_{2}^2$

The expression you're looking for is simply the sum of those 2 intensities.

Now, let's calculate the distance between one of the sources and P. Assuming that P is at a distance x, then the distance between the source and P is:

$\displaystyle D_{1}=\sqrt{d^2+x^2}$

So

$\displaystyle I_{1}(x)= \frac{S}{D_{1}^2}=\frac{S}{\sqrt{d^2+x^2}^2}=\frac {S}{d^2+x^2}$

Now you need to find the intensity due to the other source.