how many coulombs must be on one object for it to be repelled with a force of 6.0 N by a second charge of 2.0uC at a distance of 1.0 m?
Just solve for q2 in the formula
F = (k q1 q2)/d^2
There is an interactive calculator at
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html
To find the charge on the first object, we can use Coulomb's law, which states that the force between two charged objects is given by the equation:
F = k * (|q1| * |q2|) / r^2,
where F is the force, k is the electrostatic constant (k = 9.0 * 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
In this case, we are given:
- Force (F) = 6.0 N,
- Charge on the second object (|q2|) = 2.0 μC (microcoulombs),
- Distance (r) = 1.0 m.
We need to solve for the charge on the first object (|q1|).
Rearranging the equation, we have:
|q1| = (F * r^2) / (k * |q2|).
Substituting the given values:
|q1| = (6.0 N * (1.0 m)^2) / (9.0 * 10^9 N m^2/C^2 * 2.0 μC).
To simplify the calculation, let's convert the microcoulombs (μC) to coulombs (C):
1 μC = 1 * 10^-6 C.
|q1| = (6.0 N * (1.0 m)^2) / (9.0 * 10^9 N m^2/C^2 * 2.0 * 10^-6 C).
Simplifying further:
|q1| = (6.0 * 1.0) / (9.0 * 2.0 * 10^9 * 10^-6) C.
|q1| = 0.333 * 10^6 C.
Therefore, the charge on the first object must be 0.333 * 10^6 Coulombs (C) for it to be repelled with a force of 6.0 N by the second charge of 2.0 μC at a distance of 1.0 m.