two point charges are separated by a distance of three meters. the two point charges have equal magnitudes of -18 uc. Find the electric force between the two
To find the electric force between two point charges, we can use Coulomb's Law. Coulomb's Law states that the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * q1 * q2) / r^2
Where:
- F is the electric force between the two charges,
- k is the Coulomb's constant (a constant value of approximately 9 × 10^9 N m^2/C^2),
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges.
In this case, both charges have equal magnitudes of -18 μC. Since the charges are equal, we can simplify the formula to:
F = (k * q^2) / r^2
Let's substitute the given values into the formula:
F = (9 × 10^9 N m^2/C^2) * (-18 μC)^2 / (3 m)^2
Before we proceed, note that 1 μC (microcoulomb) is equal to 1 × 10^(-6) C (coulomb). So, -18 μC is equal to -18 × 10^(-6) C.
F = (9 × 10^9 N m^2/C^2) * (-18 × 10^(-6) C)^2 / (3 m)^2
Next, we simplify the expression:
F = (9 × 10^9 N m^2/C^2) * (18 × 10^(-6))^2 / (3)^2
F = (9 × 10^9 N m^2/C^2) * (18^2 × 10^(-6))^2 / (3)^2
F = (9 × 10^9 N m^2/C^2) * (18^2 × 10^(-6))^2 / 3^2
F = (9 × 10^9 N m^2/C^2) * (324 × 10^(-6))^2 / 9
F = (9 × 10^9 N m^2/C^2) * (324 × 10^(-6))^2 / 9
F = (9 × 10^9 N m^2/C^2) * (324 × 10^(-6))^2 / 9
F = (9 × 10^9 N m^2/C^2) * (104,976 × 10^(-12)) / 9
F = 9.88 × 10^(-3) N
Therefore, the electric force between the two charges is approximately 9.88 × 10^(-3) Newtons.