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, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the force (F) between two charged objects is given by the equation:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (9.0 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges on the two objects, and
r is the distance between the center of the two objects.
In this case, the charges are +1.0 C and -1.0 C, so q1 = 1.0 C and q2 = -1.0 C. The distance between the objects is 1.0 km, but it needs to be converted to meters (since k is in m^2).
Converting 1.0 km to meters:
1.0 km = 1000 m
Now we can substitute the values into the formula:
F = (9.0 x 10^9 N m^2/C^2 * |1.0 C * -1.0 C|) / (1000 m)^2
Calculate the charge product:
|1.0 C * -1.0 C| = 1.0 C^2
Simplify the equation:
F = (9.0 x 10^9 N m^2/C^2 * 1.0 C^2) / (1000 m)^2
Now, calculate the force using a calculator:
F = (9.0 x 10^9 N m^2/C^2 * 1.0 C^2) / (1000 m)^2
= 9.0 x 10^9 N m^2/C^2 / 1000^2 m^2
= 9.0 x 10^9 N / 1000^2
= 9.0 x 10^9 N / 10^6
Simplify:
F = 9.0 x 10^3 N
Therefore, the magnitude of the force that each charge exerts on the other is 9.0 x 10^3 Newtons.