The repulsive electric force between the point charges -6.36 * 10^-6 C and q has a magnitude of 1.32 N when the separation between the charges is 1.07 m. Find the sign and the magnitude of the charge q.
-2.46x 10*-5c
To find the sign and magnitude of charge q, we can use Coulomb's law, which states that the magnitude of the electric force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's law formula is given by:
F = k * |q1| * |q2| / r^2
Where:
F is the magnitude of the electric force,
k is the electrostatic constant (9 × 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the two charges, and
r is the separation between the charges.
We are given:
F = 1.32 N,
|q1| = 6.36 × 10^(-6) C,
r = 1.07 m.
Plugging these values into the formula, we can solve for |q2|.
1.32 N = (9 × 10^9 N m^2/C^2) * (6.36 × 10^(-6) C) * |q2| / (1.07 m)^2
To solve for |q2|, we need to rearrange the equation:
|q2| = (1.32 N * (1.07 m)^2) / ((9 × 10^9 N m^2/C^2) * (6.36 × 10^(-6) C))
Calculating this expression will give us the magnitude of |q2|.