# Electric Potential/Work - POint Charges on a Square

• alicemunro
In summary, two identical point charges placed on opposite corners of a square with a side length of 0.5m and a charge of +3 x 10^ -6 C each, result in a work done by the electric force of -4.7 x 10^-2 when one charge moves to an empty corner. This can be calculated using the equation W = qV = q(kq/r) = kq^2/ r, where q is the charge, V is the potential energy, k is the Coulomb constant, and r is the distance between the charges. The initial potential energy is 0, so the work done is just the final potential energy.
alicemunro

## Homework Statement

two identical point charges are on diagonally opposite corners of a square that is 0.5m on a side. Each charge is +3 x 10^ -6 C. How much work is done by the electric force when 1 charge moves to an empty corner?

## Homework Equations

W= u= qV = q(kq/r) = kq^2/ r (is this right??)

## The Attempt at a Solution

w= kq^2 / r = (k)(+3 x 10^ -6)^2 / (.5)

the real answer is -4.7 x 10^-2 but i don't know how to get that. thanks

Almost! It is the "W = u" part where you err. This U is the potential energy. The work done is the difference between the U at the beginning point and the U at the ending point.
You already have it half done.

I can confirm that your attempt at a solution is correct. The equation W= kq^2 / r is the correct formula for calculating the work done by the electric force. The negative sign in the answer indicates that the work done is in the opposite direction of the displacement of the charge. In this case, the charge is moving away from the other charge, so the work done is negative. To get the correct numerical answer, you need to use the value of the Coulomb constant, k= 8.99 x 10^9 Nm^2/C^2. When you substitute this value into the equation, you will get the correct answer of -4.7 x 10^-2 J. I hope this helps clarify your solution.

## 1. What is electric potential?

Electric potential, also known as voltage, is a measure of the potential energy per unit charge at a point in an electric field. It describes the amount of work that must be done to move a unit positive charge from infinity to that point against the electric field.

## 2. How is electric potential calculated for a point charge on a square?

The electric potential at a point on a square is calculated using the formula V = k*q/r, where V is the electric potential, k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge to the point on the square.

## 3. What is the relationship between electric potential and electric field?

Electric potential and electric field are related by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator. This means that the electric field is the negative gradient of the electric potential.

## 4. How does the electric potential change as the distance from a point charge on a square increases?

The electric potential decreases as the distance from the point charge on a square increases. This follows the inverse square law, which states that the electric potential is inversely proportional to the distance squared.

## 5. What is the work done by an external force to bring a point charge from one point to another on a square?

The work done by an external force to bring a point charge from one point to another on a square is equal to the change in electric potential energy, which is calculated by multiplying the charge of the point charge by the difference in electric potential between the two points.

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