You are playing Electric Field Hockey with the electric puck with a charge of +5.0 μC. You placed a charge of -3.0 μC to the right of the puck and the +5.0 μC charge experiences a force of 20N. What is the distance between the two charges?
To determine the distance between the two charges, we can make use of Coulomb's Law, which relates the electrostatic force between two charged objects to their charges and the distance between them.
Coulomb's Law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them:
F = k * (|q1 * q2|) / r^2
Where:
- F is the electrostatic force between the charges
- k is the electrostatic constant, approximately equal to 9 × 10^9 N·m^2/C^2
- q1 and q2 are the charges of the two objects
- r is the distance between the two charges
In this case, we are given:
- q1 = +5.0 μC (charge of the puck)
- q2 = -3.0 μC (charge to the right of the puck)
- F = 20N
Rearranging Coulomb's Law to solve for the distance (r):
r^2 = k * (|q1 * q2|) / F
Now we can substitute the given values and solve for r:
r^2 = (9 × 10^9 N·m^2/C^2) * (|+5.0 μC * -3.0 μC|) / 20N
To calculate the product of the charges, we multiply their magnitudes: 5.0 μC * 3.0 μC = 15.0 μC^2
r^2 = (9 × 10^9 N·m^2/C^2) * (15.0 × 10^-12 C^2) / 20N
= 6.75 × 10^-4 m^2
Now, taking the square root of both sides of the equation gives us:
r = √(6.75 × 10^-4 m^2)
Calculating the square root:
r ≈ 0.026 m (rounded to three decimal places)
Therefore, the distance between the charges is approximately 0.026 meters.