Two objects 18.5m apart both have the same charge. If the force on one of them is 0.4029N what is the charge (in µC) on the object?
To find the charge on the object, we can use Coulomb's Law, which 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 objects,
k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2),
q1 and q2 are the charges on the objects,
r is the distance between the objects.
In this case, we are given:
F = 0.4029 N
r = 18.5 m
q1 = q2 (both objects have the same charge)
Rearranging the formula, we can solve for the charge (q1 = q2):
q1 = (F * r^2) / (k)
Substituting the known values:
q1 = (0.4029 N * (18.5 m)^2) / (8.99 x 10^9 N m^2/C^2)
Calculating this expression will give us the charge in coulombs (C). To convert it to microcoulombs (µC), we divide the result by 10^-6 since 1 µC = 10^-6 C.
Let's calculate:
q1 = (0.4029 N * (18.5 m)^2) / (8.99 x 10^9 N m^2/C^2)
= (0.4029 N * 342.25 m^2) / (8.99 x 10^9 N m^2/C^2)
= 138.090525 / (8.0991 x 10^-9 C)
≈ 1.706 x 10^-5 C
To convert this to microcoulombs (µC), we divide by 10^-6:
q1 = 1.706 x 10^-5 C / (10^-6)
= 1.706 x 10^1 µC
≈ 17.06 µC
Therefore, the charge on each object is approximately 17.06 µC.