I've got the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

1) We've got a charge -Q at location at the origin and two charges of the same magnitude but opposite sign at [tex](a,0,0)[/tex] and [tex](0,a,0)[/tex]. Determine the total force on the charge at the origin.

2) We've got the same charge -Q at the origin but now a charge of 2Q at [tex](a,a,0)[/tex]. Again, determine the force on the charge at the origin.

Then compare your answer to the previous question

The first thing I did was to calculate the seperate forces and then add them together.

[tex]\vec{F}_1 = \frac{1}{4\pi\epsilon_0} \frac{Q^2}{a^2} \hat{x}[/tex]

[tex]\vec{F}_2 = \frac{1}{4\pi\epsilon_0} \frac{Q^2}{a^2} \hat{y}[/tex]

So the total force is given by

[tex]\vec{F} = \frac{1}{4\pi\epsilon_0} \frac{Q^2}{a^2} (\hat{x}+\hat{y})[/tex]

Now for the second question the distance between the two charges is given by [tex]\sqrt{a^2+a^2}[/tex], so the force is given by

[tex]\vec{F} = \frac{2Q^2}{4\pi\epsilon_0}\frac{a\hat{x} + a\hat{y}}{(a^2+a^2)^{\frac{3}{2}}} = \frac{2Q^2}{4\pi\epsilon_0}\frac{a\hat{x} + a\hat{y}}{2\sqrt{2}a^3} = \frac{1}{4\pi\epsilon_0}\frac{Q^2}{a^2}\frac{1}{\sqrt{2}}(\hat{x} + \hat{y})[/tex]

Now I would like to ask you if these calculations are really correct?

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# Homework Help: Simple electrostatics

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