two identical point charges are fixed to diagonally opposite corners of a square that is .5m on a side. Ecah charge is +3.0x10^-6 C. How much work is done by the elctric force as one of the charges moves to an empty corner
Well, that sounds like an electrifying situation! Let's calculate the work done by the electric force.
To solve this problem, we can make use of the equation for the electric force:
F = k * (q1 * q2) / r^2
Where:
F is the electric force
k is the electrostatic constant (9 * 10^9 N m^2/C^2)
q1 and q2 are the charges (in this case, both are +3.0x10^-6 C)
r is the distance between the charges
Since the charges are fixed to diagonally opposite corners of a square, the distance between them is the length of the diagonal of the square, which can be calculated using the Pythagorean theorem:
d = sqrt((side length)^2 + (side length)^2)
Given that the side length of the square is 0.5 m, we can substitute this into the equation for d:
d = sqrt((0.5)^2 + (0.5)^2)
d = sqrt(0.5)
Now we can plug in the values into the equation for the electric force:
F = (9 * 10^9) * ((3.0x10^-6) * (3.0x10^-6)) / (0.5)
F = (9 * 10^9) * ((9.0x10^-12) / 0.5)
F = (9 * 10^9) * (1.8x10^-12)
F = 16.2x10^-3
Finally, we can calculate the work done by multiplying the force by the displacement:
Work = F * d
Work = (16.2x10^-3) * sqrt(0.5)
Work ≈ 11.49 J
So, approximately 11.49 Joules of work is done by the electric force as one of the charges moves to an empty corner.
To calculate the work done by the electric force as one of the charges moves to an empty corner, we need to determine the magnitude of the electric force and the distance over which the force is applied.
First, let's calculate the magnitude of the electric force between two point charges. The formula to calculate the electric force is given by Coulomb's Law:
F = k * (q1 * q2) / r^2,
where:
- F is the electric force,
- k is the electrostatic constant (9.0 x 10^9 N m²/C²),
- q1 and q2 are the charges,
- r is the distance between the charges.
Since the point charges are identical and have the same magnitude (3.0 x 10^-6 C), we can simplify the formula to:
F = k * (q^2) / r^2.
Now, let's calculate the magnitude of the electric force. Substituting the given values into the formula:
F = (9.0 x 10^9 N m²/C²) * (3.0 x 10^-6 C)^2 / (0.5 m)^2.
Calculating this will give us the magnitude of the electric force between the charges.
Next, we need to determine the distance over which the force is applied. As one of the charges moves to an empty corner, the distance between the charges will increase to the length of the square's diagonal, which can be calculated using the Pythagorean theorem:
d = √(s^2 + s^2),
where s is the side length of the square.
Substituting the given value of the side length (0.5 m) into the formula will give us the distance over which the force is applied.
Once we have the magnitude of the electric force and the distance, we can calculate the work done by multiplying these two values:
work = force * distance.
Substituting the calculated values into this formula will give us the answer to the question.