What Is the Electric Potential at the Origin Given Four Point Charges?

[jehan60188]

Homework Statement

4 charges, distributed as follows

12*10$^{-6}$ C @ (-4,4)
12*10$^{-6}$ C @ (4,4)
-6*10$^{-6}$ C @ (-4,-4)
-3*10$^{-6}$ C @ (4,-4)

Calculate the potential at the origin if the potential at infinity is zero.

Homework Equations

V= U/q = -W/q = ∫E*dl = k*q/r

for multiple point charges, find V for each one, and sum them up

The Attempt at a Solution

$V1 = V2 = \frac{k*12*10^{-6}}{(4*\sqrt{2}/2)}$
$V3 = \frac{k*-6*10^{-6}}{(4*\sqrt{2}/2)}$
$V4 = \frac{k*-3*10^{-6}}{(4*\sqrt{2}/2)}$


$V1+V2+V3+V4 = \frac{k*3*10^{-6}}{4*\frac{\sqrt{2}}{2}}*(4+4-2-1) = 47676.7$


So, I factor out the k, the 3*10e-6, and the 1/(r) from each Vi, then multiply it by 4+4-2-1 =5

this answer is not right. Any pointers?

thanks!]

 

[tiny-tim]

hi jehan60188!

shouldn't r be 4√2 ? ​

 

[jehan60188]

hi jehan60188!

shouldn't r be 4√2 ? ​

4^2 + 4^2 = 32 = 4 Sqrt(2)
why, WHY did I divide by 2?!

divided my solution by 2 (since it was sqrt(2)/2 in the divisor), and got the right answer! thanks!

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