A charge of +2 X 10^-7 C is 10 cm from a charge of -6 X 10^-6 C. Find the magnitude and direction of the force of each charge.
To find the magnitude and direction of the force between two charges, we can use Coulomb's Law equation. Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
where F represents the force between the charges, k is the electrostatic constant (approximately 9 x 10^9 N*m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's calculate the force between the charges:
Given:
q1 = +2 x 10^-7 C
q2 = -6 x 10^-6 C
r = 10 cm = 0.1 m
k = 9 x 10^9 N*m^2/C^2
First, let's calculate the magnitude of the force:
F = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N*m^2/C^2) * ((2 x 10^-7 C) * (6 x 10^-6 C)) / (0.1 m)^2
Calculating this expression, we get:
F = (9 x 10^9 N*m^2/C^2) * (1.2 x 10^-12 C^2) / 0.01 m^2
= 1.08 x 10^-2 N
So, the magnitude of the force is approximately 1.08 x 10^-2 N.
Next, we need to determine the direction of the force. The force between the charges is attractive if the charges have opposite signs and repulsive if they have the same sign.
Given that the charge q1 is positive and the charge q2 is negative, the direction of the force is attractive, meaning it pulls the charges together.
In summary, the magnitude of the force between the charges is approximately 1.08 x 10^-2 N, and the direction of the force is attractive, pulling the charges together.