two point charges have a total charge of 277 µC. When placed 2.00 m apart, the force each exerts on the other is 20.8 N and is repulsive.
what are the charges on both?
Let the two charges be Q1 and Q2
Q1 + Q2 = 277 µC
k*Q1*Q2 /R^2 = 20.8 Newtons
Two equations; two unknowns.
k is the Coulomb constant. Look it up if you need to.
R = 2.00 m
Take it from there; it's just algebra.
To determine the charges on both point charges, we can use Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote the charges as q1 and q2, and the distance between them as r.
From the given information:
- The total charge of both point charges is 277 µC, which means q1 + q2 = 277 µC.
- The force exerted on each other is 20.8 N and is repulsive. Since the force is repulsive, the charges should have the same sign.
Using Coulomb's Law, we can write the equation for the force between the charges:
F = k * (|q1| * |q2|) / r^2
where F is the force, k is the electrostatic constant, and r is the distance between the charges.
To proceed, we need to know the value of the electrostatic constant, k. Its value is 8.99 × 10^9 N·m^2/C^2.
Substituting the given force and distance into the equation, we get:
20.8 N = (8.99 × 10^9 N·m^2/C^2) * (|q1| * |q2|) / (2.00 m)^2
Simplifying the equation:
20.8 N = (8.99 × 10^9 N·m^2/C^2) * (|q1| * |q2|) / 4.00 m^2
Now, we can substitute q2 = 277 µC - q1 into the equation because we know that q1 + q2 = 277 µC:
20.8 N = (8.99 × 10^9 N·m^2/C^2) * (|q1| * |(277 µC - q1)|) / 4.00 m^2
Simplifying further, we can solve this equation to find the values of q1 and q2.