You remove two socks from a hot dryer and find that they repel with forces of 0.003 N when they’re 4 cm apart. If they have equal charges, how much charge does each sock have?
To determine the charge on each sock, we can use 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.
Coulomb's law can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the force of repulsion,
k is the Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2),
q1 and q2 are the charges on the two socks,
and r is the distance between the socks.
From the question, we know that the force of repulsion between the socks is 0.003 N when they are 4 cm (0.04 m) apart.
Plugging in the known values into Coulomb's law:
0.003 N = (9 x 10^9 Nm^2/C^2) * (q1 * q2) / (0.04 m)^2
Simplifying:
0.003 N = (9 x 10^9 Nm^2/C^2) * (q1 * q2) / 0.0016 m^2
0.003 N * 0.0016 m^2 = (9 x 10^9 Nm^2/C^2) * (q1 * q2)
0.0048 Nm^2/C = q1 * q2
To find the charge on each sock, we need to determine the charges q1 and q2. Since the socks have equal charges, we can assume q1 = q2 = q.
Therefore,
0.0048 Nm^2/C = q^2
Taking the square root of both sides:
q = sqrt(0.0048 Nm^2/C)
Calculating the value of q using a calculator:
q ≈ 0.069 C
Therefore, each sock has a charge of approximately 0.069 C.