A point charge with a charge of q1=2.60uC is held stationary at the origin. A second point charge with charge q2=-4.70uC moves from the point. x=0.140m, y=0 to the point
x=0.230m, y=0.290m
How much work is done by the electric force on q2?
To find out the amount of work done by the electric force on q2, we can use the formula:
Work = Force * Displacement * Cos(theta)
In this case, the work done by the electric force on q2 is calculated using the force between the two charges (given by Coulomb's Law), the displacement of q2, and the cosine of the angle between the force and displacement vectors.
Step 1: Calculate the force between the charges.
The force between two charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
where F is the force, k is Coulomb's constant (9 * 10^9 N*m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, q1 = 2.60 uC and q2 = -4.70 uC. We need to convert these charges into coulombs:
q1 = 2.60 * 10^-6 C
q2 = -4.70 * 10^-6 C
The distance between the charges is given by the displacement between the two points:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given coordinates, r = sqrt((0.230 - 0.140)^2 + (0.290 - 0)^2).
Step 2: Calculate the work done.
The work done by the electric force can be calculated using the formula provided earlier:
Work = Force * Displacement * Cos(theta)
Here, the force is given by Coulomb's Law, the displacement is the distance between the two points, and theta is the angle between the force and displacement vectors. In this case, theta is 0 degrees since the displacement is along the x-axis.
Therefore, Work = F * (x2 - x1)
Substituting the calculated force and displacement, we can find the work done.
Work is conservative, so do the x first, then the y.
work=INT f.dx + int f.dy
= INTkq1q2/x^2 dx+ int kq1q2/y^2 dy
= kq1q1 (1/x)over limits + kq1q2 (1/y)over limits
limits x .140 to .230 ; y 0 to .290