Two electrostatic point charges of +51.0 µC
and +56.0 µC exert a repulsive force on each
other of 165 N.
What is the distance between the two
charges? The value of the Coulomb constant
is 8.98755 × 10^9 N · m^2
/C^2
.
Answer in units of m.
To find the distance between the two charges, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's Law formula is given by:
F = k * (|q1*q2| / r^2)
Where:
F is the electrostatic force
k is the Coulomb constant (8.98755 × 10^9 N · m^2 / C^2)
|q1*q2| is the product of the magnitudes of the two charges
r is the distance between the charges
Given:
Magnitude of charge 1, q1 = +51.0 µC (microcoulombs)
Magnitude of charge 2, q2 = +56.0 µC (microcoulombs)
Electrostatic force, F = 165 N
First, convert the charges from microcoulombs to coulombs:
q1 = 51.0 µC = 51.0 × 10^-6 C
q2 = 56.0 µC = 56.0 × 10^-6 C
Rearrange the formula to solve for r:
r = √(k * (|q1*q2| / F))
Substitute the given values:
r = √(8.98755 × 10^9 N · m^2 / C^2 * (|51.0 × 10^-6 * 56.0 × 10^-6|) / 165 N)
Calculate the product of the charges inside the square root:
|r1*r2| = |51.0 × 10^-6 * 56.0 × 10^-6| = 2.856 × 10^-9 C^2
Now, substitute the calculated values:
r = √(8.98755 × 10^9 N · m^2 / C^2 * 2.856 × 10^-9 C^2 / 165 N)
Simplify:
r = √((8.98755 × 10^9 * 2.856 × 10^-9) / 165) m
After evaluating the expression inside the square root and simplifying further, we get:
r = √((25.69911) / 165) m
Finally, calculate the square root:
r ≈ √(0.15575) m
The distance between the two charges is approximately:
r ≈ 0.394 m