Two objects with charges of +1.0 c and -1.0 c 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 between two charged objects, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the force between two charges is proportional to the product of their 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 charges,
k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2),
q1 and q2 are the charges of the two objects, and
r is the distance between the charges.
In this case, the charges are +1.0 C and -1.0 C, and the distance between them is 1.0 km (which we need to convert to meters, since the SI unit for distance is meters).
First, let's convert 1.0 km to meters:
1.0 km = 1,000 meters
Now, let's substitute the values into the equation and calculate the force:
F = (9.0 x 10^9 Nm^2/C^2) * (1.0 C * -1.0 C) / (1,000 m)^2
F = (9.0 x 10^9 Nm^2/C^2) * (-1.0 C^2) / 1,000,000 m^2
F = -9.0 x 10^3 N
Therefore, the magnitude of the force that either charge exerts on the other is 9.0 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 magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula is given as:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electrostatic force,
k is the Coulomb's constant (9 × 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges,
and r is the distance between the charges.
In this case, we have two charges, q1 = +1.0 C and q2 = -1.0 C, separated by a distance of r = 1.0 km = 1.0 × 10^3 m.
Plugging these values into the formula:
F = (9 × 10^9 Nm^2/C^2) * (|1.0 C| * |-1.0 C|) / (1.0 × 10^3 m)^2
Simplifying the calculation:
F = (9 × 10^9 Nm^2/C^2) * (1.0 C) * (1.0 C) / (1.0 × 10^3 m)^2
F = (9 × 10^9 Nm^2/C^2) * 1.0 C^2 / 1.0 × (10^3 m)^2
F = 9 × 10^9 Nm^2 / (1.0 × 10^3 m)^2
F = 9 × 10^9 Nm^2 / 1.0 × 10^6 m^2
F = 9 × 10^3 N
Therefore, the magnitude of the force that either charge exerts on the other is 9 × 10^3 N.