Three collinear charges +7.0 x10^-5 C , +4.8 x10*-5 C, and -8.0 x 10^-5 C exert forces on each other. The first and second charges are 35.0 cm apart. The second and third charges are 35.0 cm apart. What is the magnitude and charge of the total force on the third charge?
I know the answer is F=-380 N , but I'm confused on how to get the answer.
To solve this problem, we can use 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. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
where:
F = force between the charges (in Newtons)
k = Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2)
q1, q2 = charges of the two objects (in Coulombs)
r = distance between the charges (in meters)
Let's break down the problem step by step:
1. Calculate the force between the first and second charges:
q1 = +7.0 x 10^-5 C
q2 = +4.8 x 10^-5 C
r = 35.0 cm (or 0.35 m)
Plugging these values into Coulomb's law:
F1-2 = (8.99 x 10^9 N m^2/C^2) * ((7.0 x 10^-5 C) * (4.8 x 10^-5 C)) / (0.35 m)^2
Simplifying, we find:
F1-2 ≈ 272.65 N (approximately)
2. Calculate the force between the second and third charges:
q2 = +4.8 x 10^-5 C
q3 = -8.0 x 10^-5 C
r = 35.0 cm (or 0.35 m)
Plugging these values into Coulomb's law:
F2-3 = (8.99 x 10^9 N m^2/C^2) * ((4.8 x 10^-5 C) * (-8.0 x 10^-5 C)) / (0.35 m)^2
Simplifying, we find:
F2-3 ≈ -532.20 N (approximately)
3. Find the total force on the third charge:
Since forces are vector quantities, we need to consider both magnitude and direction. The magnitudes of the forces are:
|F1-2| ≈ 272.65 N
|F2-3| ≈ 532.20 N
Since the direction of both forces is opposite, we subtract the magnitudes to obtain the net force:
|F3| = |F2-3| - |F1-2|
= 532.20 N - 272.65 N
Simplifying, we find:
|F3| ≈ 259.55 N
However, since the question asks for the magnitude and charge of the total force, we need to remember that the force is negative due to the sign of the third charge. Therefore, the magnitude and charge of the total force are:
|F3| = 259.55 N (magnitude)
F3 = -259.55 N (force with direction)
So, the magnitude and charge of the total force on the third charge are approximately 259.55 N and -259.55 N, respectively.