Help Needed: Finding Voltage at x with Binomial Expansion

[rei]

I've been struggling with this problem for hours. I don't know what I did was wrong. Someone please give me a hint or point out where I did was wrong. Thanks a lot.

There are three charges : the first charge of +2Q locates at (0,0), the second charge of -Q locates at (0,d), the third charge of -Q locate (0,-d). Find the voltage at position x (X,0) when X>>>d. Use binomial theorem to expand the answer. Suppose that at x=2m, V= 160, find the approximate value of V at x=4. Assume that d <<<2m

I don't know how to insert a drawing in here. But according to the problem, the three charge would all on the y-axis and the point where we have to find the voltage is going to be on the x axis. I found:

V = (2Q/4*pi*epsilon) * (1/x - 1/sqrt{d^2+x^2})

Even after I use binomial expansion, I still couldn't cancel out d. I assume that somehow I have to cancel out d cause later on I have to estimate V without any exact value for d.

Can I anyone help me please. Thanks a lot!

 

[rei]

Can anyone just give me a hint please

 

[thepatientmental]

First of all, don't worry about making mistakes or struggling with a problem. It's all part of the learning process and seeking help is a great way to improve your understanding. As for your problem, it seems like you are on the right track by using the binomial expansion. However, it's important to remember that the binomial expansion is an approximation and may not give an exact answer.

One potential issue with your solution is that you may have missed a negative sign when expanding the terms. Also, be sure to use the correct signs for the charges when plugging in values. Another thing to consider is that the binomial expansion may only be accurate for small values of x, so using it for larger values may not give an accurate result.

If you are still struggling, it might be helpful to break down the problem into smaller parts and work through them individually. Also, try double checking your calculations and make sure you are using the correct formula for voltage. And don't forget to take into account the direction of the electric field due to the charges.

Overall, don't get discouraged and keep trying. You can also seek help from a tutor or classmate who may have a different perspective on the problem. Good luck!