A charge of +1q is fixed to one corner of a square, while a charge of -3q is fixed to the diagonally opposite corner. Expressed in terms of q, what charge should be fixed to the center of the square, so the potential is zero at each of the two empty corners?



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Physics please clarify - bobpursley, Tuesday, September 4, 2007 at 9:06pm
stop looking for formulas. Voltage is q/distance. It is a scalar, so you add all the contributing charges. In this case,

voltage at empty corner= voltage from each charge
0= q/s -3q/s + x/d
where s is the side distance, and d is the distance from the empty corner to the center. d=.707s.
solve for x.

I am sorry for being such a bother,I appreciate all of the help you've given to me but I am still not getting this one! I think I am over thinking this problem. This is what i did so far please tell me if I am on the right track:

q/s - 3q/s + X/d = 0

-2q/s + X/d = 0

X/d = 2q/s

X= (2q/s)(d)

from here I am stumped.

I answered this once before. You have a geometrical relationship between a and s, d=.707s , so d/s can be converted to a constant. This gives you an equation that relates X to q.

To solve this problem, you are on the right track so far. You correctly set up the equation:

q/s - 3q/s + X/d = 0

Next, simplify the equation:

-2q/s + X/d = 0

Multiply both sides of the equation by sd:

sd * (-2q/s + X/d) = 0

This will give you:

-2qd + Xs = 0

Now, we have a relationship between X and q that we can solve for. Since we know that d = 0.707s, substitute this value into the equation:

-2q(0.707s) + Xs = 0

-1.414qs + Xs = 0

Now, factor out the s:

s(-1.414q + X) = 0

Since we want the potential to be zero at each of the two empty corners, we know that the potential contribution from each charge must cancel each other out. In other words, the potential at the empty corners must be the negative of each other. Therefore, the value of X must be equal to -1.414q.

So, the charge that should be fixed to the center of the square to make the potential zero at each of the two empty corners is -1.414q, expressed in terms of q.