A -6 x10^-6 point charge is .030 m from another point charge and experiences a repulsive fore of 180 N what is the magnitude of the other charge
recall that F = k(q1 q2)/d^2
now just plug and chug, after looking up k.
To find the magnitude of the other charge, we can use Coulomb's Law, which states that the 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.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
In this case, we know the following information:
F = 180 N
|q1| = 6 x 10^-6 C (since the given charge is -6 x 10^-6 C, we take its magnitude)
r = 0.030 m
Substituting these values into the formula and solving for |q2|, we have:
180 N = (9 x 10^9 Nm^2/C^2) * ((6 x 10^-6 C) * |q2|) / (0.030 m)^2
Now, we can solve for |q2|:
|q2| = (180 N * (0.030 m)^2) / (9 x 10^9 Nm^2/C^2 * 6 x 10^-6 C)
Calculate the expression:
|q2| = (180 N * 0.0009 m^2) / (54 x 10^-6 Nm^2/C)
Simplify the expression:
|q2| = 0.00306 C
Therefore, the magnitude of the other charge is 0.00306 C.