Two objects with charges of +1.0 and -1.0 are separated by 1.0km. Find the magnitude of the force that either charge exerts on the other.
To find the magnitude of the force that each charge exerts on the other, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the force between the two charges,
k is the electrostatic constant (k ≈ 9 x 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
In this case, the magnitudes of the charges are both 1.0 (|q1| = 1.0 and |q2| = 1.0) and the distance between them is 1.0 km = 1000 m (r = 1000 m).
Plugging these values into the equation, we get:
F = (9 x 10^9 N m^2/C^2) * (1.0 * 1.0) / (1000^2)
Simplifying further, we have:
F = (9 x 10^9 N m^2/C^2) / 1,000,000
Calculating this, we find:
F ≈ 9 x 10^-3 N
Therefore, the magnitude of the force that either charge (with a charge of +1.0 or -1.0) exerts on the other is approximately 9 x 10^-3 Newtons.
To find the magnitude of the force that either charge exerts on the other, we can use Coulomb's law. Coulomb's law states that the 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 force between the charges, |q1| and |q2| are the magnitudes of the charges, r is the distance between the charges, and k is the electrostatic constant.
The electrostatic constant, k, has a value of 9 × 10^9 N∙m^2/C^2.
Given:
Charges |q1| = +1.0 (Coulombs)
Charges |q2| = -1.0 (Coulombs)
Distance r = 1.0 km = 1000 m
Let's substitute the values into the formula and solve for F:
F = (9 × 10^9 N∙m^2/C^2) * ((+1.0 C) * (-1.0 C)) / (1000 m)^2
Calculating the expression:
F = (9 × 10^9 N∙m^2/C^2) * (-1.0 C^2) / (1000 m)^2
F = -9 × 10^9 N∙m^2 / (1000 m)^2
F = -9 × 10^9 N∙m^2 / 1000000 m^2
F = -9000 N∙m^2 / m^2
F = -9000 N
The magnitude of the force that either charge exerts on the other is 9000 Newtons.