Two point charges have a total charge of 505 µC. When placed 1.10 m apart, the force each exerts on the other is 19.3 N and is repulsive. What is the charge on each? (Round your answers to the nearest µC.)
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Let the two charges be Q1 and Q2.
In this case, Q2 = 505*10^-6 - Q1
Since the force is replusive, they both have the same sign.
Coulomb's Law tells you that
19.3 N = k*Q1*Q2/R^2, where R = 1.1 m
Substitute 505*10^-6 - Q1 for Q2 and solve for Q1.
You will have to look up k. It is something like 8.99*10^9 N(m^2/C^2), but I don't trust my memory.
Use Coulomb's law:
F=(1/(4πε0))*(q1*q2/r²)
where
ε0=8.85*10^-12 C² N-1 m-2
q1,q2 are charges (C)
r=distance between the charges (m)
The equation applies when the distance r is large compared to the size of the charged particles.
The force is repulsive when positive, and negative when attractive.
Thus if one charge is q, the other charge would be .000505-q.
We have
F=q(.000505-q)/(4π&epsilon0)
where all quantities are known except q.
Solve for q.
To find the charge on each point charge, we can make use of Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them:
F = k * (|q1| * |q2|) / r^2
where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, we are given the force and the distance between the charges, so we can rearrange the equation to solve for the product of the charges:
|q1| * |q2| = (F * r^2) / k
Since the charges are given as opposite signs (repulsive force), we can assume that one charge is positive and the other is negative. Let's assign |q1| as the positive charge and |q2| as the negative charge.
Now, let's substitute the given values into the equation:
|q1| * |q2| = (19.3 N * (1.10 m)^2) / (9 * 10^9 N*m^2/C^2)
Simplifying the equation:
|q1| * |q2| = 24.22 * 10^-9 C^2
Since we are given that the total charge of both charges is 505 µC, we can rewrite the equation as:
|q1| * |q2| = (505 * 10^-6 C)^2
Setting both equations equal to each other:
24.22 * 10^-9 C^2 = (505 * 10^-6 C)^2
Solving for |q1|:
|q1| = sqrt((24.22 * 10^-9 C^2) / (505 * 10^-6 C))
|q1| ≈ 31.03 µC
Since |q2| is the negative charge, its magnitude is the same:
|q2| ≈ -31.03 µC
Therefore, the charge on each point charge is approximately 31.03 µC.