Posted by Mary on Monday, September 3, 2007 at 12:40pm.
download mp3 free instrumental remix
A charge of +2q 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?
For Further Reading
Physics - bobpursley, Sunday, September 2, 2007 at 11:10am
Potential is a scalar, so you can just add all four contributions.
Vt= -3q/r + 2q/r + 2X/r=0
solve for charge X
when i use the formula i can up with +1q and the system is saying that the answer is incorrect.
For Further Reading
Physics please clarify - drwls, Monday, September 3, 2007 at 1:17pm
The equation you should be solving is
2q/a -3q/a + (sqrt 2)x/a = 0
Where a is the length of a side of the square. The corners with charges are a distance "a" away from the empty corners, but the center charge x is closer.
Multiplying bith sides by a gives
-q + sqrt 2 * x = 0
x = 0.707 q
Physics please clarify - Mary, Monday, September 3, 2007 at 4:39pm
Can you please explain how you get to x=0.707q.
I got how you got up to -q+sgrt2*X=0 but i keep coming up with a different answer than 0.707q.
For Further Reading
Physics please clarify - bobpursley, Monday, September 3, 2007 at 8:37pm
I misread the problem, thinking you wanted the potential zero at the center, that is why all my distances were the same.
Here, the potential at the two corners is zero. Let s be the side length..so the diagonal length from the corner to the center is s*1/sqrt2
0= -3q/s + +2q/s+ X/(s*1/sqrt2)
then q/sqrt2=X the charge at each corner, or X=.707q at each corner
Physics please clarify - Mary, Monday, September 3, 2007 at 9:34pm
The answer 0.707q is correct but I am still not understanding how to get to that answer.
I have another problem just like this one but with different values for q. When I use the formula above I am coming up with an incorrect answer. Please help. My question is:
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?
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.
To solve this problem, we need to calculate the charge that should be fixed to the center of the square so that the potential is zero at each of the two empty corners.
Let's start by considering the potential due to each charge individually. The potential due to a point charge is given by the formula V = k * (q / r), where V is the potential, k is the electrostatic constant (approximately 9 x 10^9 N m^2/C^2), q is the charge, and r is the distance from the charge.
In this case, the charge at the corner is +2q, and the charge at the diagonally opposite corner is -3q. We want the potential to be zero at each of the empty corners.
We can calculate the potential due to each of these charges separately. The charge at the corner is a distance equivalent to the side length (let's call it "a") away from each empty corner, so the potential due to the +2q charge at each empty corner is given by V1 = k * (2q / a).
Similarly, the charge at the diagonally opposite corner is a distance of sqrt(2) * a away from each empty corner, so the potential due to the -3q charge at each empty corner is given by V2 = k * (-3q / sqrt(2) * a).
Now, to ensure that the total potential is zero at each empty corner, we need to find the charge (let's call it "x") at the center of the square. The center charge is a distance of sqrt(2) * a / 2 away from each empty corner, so the potential due to the center charge at each empty corner is given by V3 = k * (x / sqrt(2) * a / 2).
Since the total potential at each empty corner should be zero, we can write the equation:
V1 + V2 + V3 = 0
Substituting the expressions for V1, V2, and V3, we get:
k * (2q / a) + k * (-3q / sqrt(2) * a) + k * (x / sqrt(2) * a / 2) = 0
Simplifying the equation, we get:
2q / a - 3q / sqrt(2) * a + x / sqrt(2) * a / 2 = 0
Multiplying through by "a" to remove the denominator, we get:
2q - 3q / sqrt(2) + x / sqrt(2) * a = 0
Simplifying further, we get:
2q - 3q / sqrt(2) + x / sqrt(2) * a = 0
To find the charge "x" at the center, we need to isolate it on one side of the equation. Let's rearrange the equation:
x / sqrt(2) * a = 3q / sqrt(2) - 2q
x = (3q - 2q) / (sqrt(2) * a)
Simplifying further, we get:
x = q / (sqrt(2) * a)
Therefore, the charge that should be fixed to the center of the square, so the potential is zero at each of the two empty corners, is x = q / (sqrt(2) * a).
Now, let's apply this equation to your second problem:
In your second problem, we have a charge of +1q fixed to one corner of a square, and a charge of -3q fixed to the diagonally opposite corner. We want to find the charge "x" that should be fixed to the center of the square.
Following the same process as before, we substitute the values into the equation:
x = (3q - 1q) / (sqrt(2) * a)
Simplifying further, we get:
x = 2q / (sqrt(2) * a)
Therefore, the charge that should be fixed to the center of the square, so the potential is zero at each of the two empty corners, is x = 2q / (sqrt(2) * a).