Charges in Right Triangle

Electricity and Magnetism Level 3

Three equal charges are placed in such a way that they form a right triangle with sides $3\text{ cm}, 4\text{ cm}, 5\text{ cm}.$ Each charge has a magnitude of $2\times 10^{-6}\text{C}$ .

Find the net force acting on the charge at the right angle.

Details and assumptions:

Take $\dfrac 1{4\pi\epsilon_0} = 9\times 10^9\text{ Nm}^2/\text{C}^2$ .
Round your answer to the nearest integer.

The answer is 46.

1 solution

Muhammad Arifur Rahman
Jan 13, 2016

At the corner, two forces are acting making an angle of 90 degrees between them. And the other two charges are 3cm and 4cm away from the corner charge.

Now given, $k=\frac{1}{4\pi \epsilon_0}=9\times 10^9 Nm^2/C^2$ $q=2\mu C$ $r_1=3cm=0.03m$ $r_2=4cm=0.04m$

So, $F=\sqrt{(\frac{kq^2}{r_1^2})^2+(\frac{kq^2}{r_2^2})^2}$ $=kq^2\sqrt{\frac{1}{r_1^4}+\frac{1}{r_2^4}}$

Plugging the values, $F=45.893N$ After rounding up to the nearest integer, $F=\boxed{46N}$

Would someone like to elaborate the solution a little bit more?

arifuzzaman arif - 5 years, 5 months ago

Which part exactly confuses you?

Sravanth C. - 5 years, 5 months ago

Sravanth, I think I should've uploaded a diagram of this system. You can add that picture in the problem statement, but that will make the problem easy.

Lemme see what I can do.

Muhammad Arifur Rahman - 5 years, 5 months ago

@Muhammad Arifur Rahman – Yeah, that's why I didn't put a diagram.

Sravanth C. - 5 years, 5 months ago

I will be clarifying it soon, OK!

Muhammad Arifur Rahman - 5 years, 5 months ago

@Sravanth - Please modify the unit of electrostatic constant in the problem statement. It would be $Nm^2/C^2$ instead of $NC^2/m^2$ !

Muhammad Arifur Rahman - 5 years, 5 months ago

Thnaks! I've edited it!

Sravanth C. - 5 years, 5 months ago

So nice! But you still haven't supported my solution with your vote.

Muhammad Arifur Rahman - 5 years, 5 months ago

@Muhammad Arifur Rahman – Oh my! I forgot that, sorry!

Sravanth C. - 5 years, 5 months ago

@Sravanth C. – ……Waiting for your next awesome problem!

Muhammad Arifur Rahman - 5 years, 5 months ago

Oh . I forgot to convert the measurments

Abhinav AV - 1 year ago

Charges in Right Triangle

The answer is 46.

1 solution

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