What is the electric force between a +2 µC point charge and a –2 µC point charge if they are separated by a distance of 5.0 cm? Show your work. (µC = 1.0 × 10–6 C)
Have you read about Coulomb's law? If not, it's time you did.
F = k*Q1*Q2/R^2
In your case, Q1 = -Q2 = 2.0*10^-6 Coulombs
R = 5.0*10^-2 meters
k is the "Coulomb constant",
8.99*10^9 N*m^2*/C^2
Solve for F in Newtons.
The force will be attractive since the charges have opposite sign.
To find the electric force between two point charges, we can use Coulomb's Law:
Electric force (F) = (k * q1 * q2) / r^2
Where:
- F is the electric force
- k is the Coulomb's constant, approximately 9 × 10^9 Nm^2/C^2
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
Given:
- q1 = +2 µC = +2 × 10^-6 C
- q2 = -2 µC = -2 × 10^-6 C
- r = 5.0 cm = 5.0 × 10^-2 m
- k = 9 × 10^9 Nm^2/C^2
Let's substitute these values into Coulomb's Law to calculate the electric force:
F = (k * q1 * q2) / r^2
= (9 × 10^9 Nm^2/C^2 * +2 × 10^-6 C * -2 × 10^-6 C) / (5.0 × 10^-2 m)^2
= (9 × 10^9 Nm^2/C^2 * -4 × 10^-12 C^2) / (25 × 10^-4 m^2)
= -3.6 × 10^-3 N
Therefore, the electric force between the +2 µC point charge and the -2 µC point charge, separated by a distance of 5.0 cm (or 5.0 × 10^-2 m), is approximately -3.6 × 10^-3 N.
To calculate the electric force between the two point charges, we can use Coulomb's law. Coulomb's law states that the electric force between two charged objects is directly proportional to the product of their 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 charges,
k is the electrostatic constant (9.0 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the two point charges, and
r is the distance between the point charges.
In this case, q1 = +2 µC = 2 × 10^-6 C and q2 = -2 µC = -2 × 10^-6 C. The distance r is given as 5.0 cm = 5.0 × 10^-2 m.
Plugging in these values into the formula:
F = (9.0 × 10^9 N m^2/C^2) * ((2 × 10^-6 C) * (-2 × 10^-6 C)) / (5.0 × 10^-2 m)^2
Simplifying:
F = (9.0 × 10^9 N m^2/C^2) * (-4 × 10^-12 C^2) / (2.5 × 10^-4 m^2)
F = -1.8 × 10^-3 N
Therefore, the electric force between the +2 µC and -2 µC point charges is -1.8 × 10^-3 N. (Note: The negative sign indicates that the force is attractive.)