TWO identical point charges are fixed to a diagonally opposite corners of a square with sides 50Cl3.Each charge is 3×10^-6.calculate the amount of work done by the electric force as one of the charges is moved to any empty corner.
To calculate the amount of work done by the electric force as one of the charges is moved to an empty corner of the square, we need to consider the equation for the work done by an electric force.
The equation for the work done by an electric force is given by:
Work = Force * Distance * cos(theta)
where:
- Work is the amount of work done by the electric force
- Force is the magnitude of the electric force between the charges
- Distance is the distance over which the charge is moved
- theta is the angle between the direction of the force and the direction of the displacement
In this case, since the two charges are identical and fixed to diagonally opposite corners of the square, the distance between the charges is the length of one side of the square, which is 50 Cl^3.
Now, let's calculate the force between the charges using Coulomb's law:
Force = (k * |q1 * q2|) / r^2
where:
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges (3 x 10^-6 C in this case)
- r is the distance between the charges (50 Cl^3 in this case)
Substituting the values into the equation, we get:
Force = (9 x 10^9 Nm^2/C^2 * |3 x 10^-6 C * 3 x 10^-6 C|) / (50 Cl^3)^2
Simplifying, we have:
Force = (9 x 10^9 Nm^2/C^2 * 9 x 10^-12 C^2) / (50 Cl^3)^2
= 729 x 10^-3 N / (50 Cl^3)^2
Now that we have the force, we can calculate the work done. Since the two charges have the same charge, they will repel each other, and the angle between the direction of the force and the direction of the displacement will be 180 degrees (or pi radians).
Work = Force * Distance * cos(theta)
= 729 x 10^-3 N / (50 Cl^3)^2 * 50 Cl^3 * cos(180 degrees)
= -729 x 10^-3 N
The negative sign indicates that the work done by the electric force is negative, which means that energy is being lost as the charges repel each other.
Therefore, the amount of work done by the electric force as one of the charges is moved to an empty corner of the square is -729 x 10^-3 N.