find the force if f between charges of 100mc -50mc located 50cm a part?
To calculate the force (F) between two charges, we can use Coulomb's Law. Coulomb's Law states that the force (F) between two charges (q1 and q2) separated by a distance (r) is proportional to the product of the charges and inversely proportional to the square of the distance. The formula is:
F = k * (|q1 * q2|) / r^2
where:
F is the force between the charges,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the two charges,
|r| is the distance between the charges.
Given:
Charge 1 (q1) = 100 mc (microcoulombs)
Charge 2 (q2) = -50 mc (microcoulombs)
Distance (r) = 50 cm (centimeters)
Now, we need to convert the charges from microcoulombs (mc) to coulombs (C) and the distance from centimeters (cm) to meters (m) because the SI unit for charge is coulombs and distance is meters.
1 C = 1 x 10^-6 C (microcoulombs)
1 m = 1 x 10^-2 m (centimeters)
Charge 1 (q1) = (100 mc) * (1 x 10^-6 C/mc) = 100 x 10^-6 C = 0.1 x 10^-4 C
Charge 2 (q2) = (-50 mc) * (1 x 10^-6 C/mc) = -50 x 10^-6 C = -0.05 x 10^-4 C
Distance (r) = (50 cm) * (1 x 10^-2 m/cm) = 50 x 10^-2 m = 0.5 x 10^-1 m
Now we substitute these values into Coulomb's Law:
F = (9 x 10^9 Nm^2/C^2) * (|0.1 x 10^-4 C * (-0.05 x 10^-4 C)|) / (0.5 x 10^-1 m)^2
Simplifying the equation further:
F = (9 x 10^9 Nm^2/C^2) * (0.1 x 10^-4 C * 0.05 x 10^-4 C) / (0.5 x 10^-1 m)^2
F = (9 x 10^9 Nm^2/C^2) * (0.1 x 0.05 x (10^-4)^2) / ((0.5 x 10^-1)^2)
F = (9 x 10^9 Nm^2/C^2) * (0.005 x 10^-8) / (0.25 x 10^-2)
F = (9 x 0.005) / (0.25) x (10^9 x 10^-8 / 10^-2) N
F = (45 / 0.25) x 10^1 N
F = 180 N
Therefore, the force (F) between the charges of 100 mc and -50 mc located 50 cm apart is 180 Newtons.