If the force of repulsion between two socks is .003 and they are 2 cm apart what is the charge on each sock
To determine the charge on each sock, we can make use of Coulomb's law, which states that the force of repulsion 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 mathematical form of Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
F is the force of repulsion (0.003 N in this case)
k is the electrostatic constant (approximately 9 × 10^9 N·m^2/C^2)
q1 and q2 are the charges on the socks (what we're trying to find)
r is the distance between the socks (2 cm, or 0.02 m)
Rearranging the equation, we have:
q1 * q2 = (F * r^2) / k
Plugging in the given values:
q1 * q2 = (0.003 * (0.02)^2) / (9 × 10^9)
Now, since both socks have the same charge, we can write:
q^2 = (0.003 * (0.02)^2) / (9 × 10^9)
Taking the square root of both sides gives us:
q = sqrt((0.003 * (0.02)^2) / (9 × 10^9))
Calculating this expression will give us the charge on each sock.