Two positive charges, each of magnitude 2 10-6 C, are located a distance of 17 cm from each other.
(a) What is the magnitude of the force exerted on each charge?
To find the magnitude of the force exerted on each charge, we can use Coulomb's Law equation:
F = (k * q1 * q2) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 9 x 10^9 N.m^2/C^2),
q1 and q2 are the magnitudes of the charges,
r is the distance between the charges.
Given:
q1 = q2 = 2 x 10^-6 C (magnitude of each charge),
r = 17 cm = 0.17 m (distance between the charges).
Plugging in these values into the equation, we have:
F = (9 x 10^9 N.m^2/C^2 * 2 x 10^-6 C * 2 x 10^-6 C) / (0.17 m)^2
Simplifying this equation, we have:
F = (4 x 10^-6 N.m^2/C^2) / (0.17 m)^2
F = 8 x 10^-12 N.m^2/C^2 / 0.0289 m^2
F = 2.769 x 10^-10 N
Therefore, the magnitude of the force exerted on each charge is approximately 2.769 x 10^-10 N.
To find the magnitude of the force exerted on each charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes 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 charges, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the electrostatic constant.
In this case, we are given that the charges have a magnitude of 2 * 10^-6 C and are located a distance of 17 cm, which is equivalent to 0.17 m.
The electrostatic constant, k, is approximately 9 * 10^9 N m^2/C^2.
Substituting the given values into the formula, we have:
F = (9 * 10^9 N m^2/C^2) * ((2 * 10^-6 C)^2) / (0.17 m)^2
Calculating the expression inside the parentheses first:
F = (9 * 10^9 N m^2/C^2) * (4 * 10^-12 C^2) / (0.17 m)^2
F = (9 * 4 * 10^-3) / (0.17)^2 N
F = (36 * 10^-3) / 0.0289 N
F = 1.2478 N
Therefore, the magnitude of the force exerted on each charge is approximately 1.25 N.