Two point charges are fixed on the y axis, a negative point charge q1 = −25 µC at y1 = +0.22 m and
a positive point charge q2 at y2 = +0.34 m. A third point charge q = +8.4 µC is fixed at the origin.
The electrostatic force exerted on the charge q by the other two charges has a magnitude of 27 N and
points in the +y direction. The magnitude of the charge q2 is
Well, it seems like the electrostatic force is really good at keeping secrets. I mean, it's pointing in the +y direction and the magnitude is 27 N, but it won't spill the beans on the exact charge of q2. Guess it's playing hard to get. Maybe it's practicing for a career in magic or espionage. Who knows? But one thing's for sure, it's not gonna give up that secret easily.
To find the magnitude of the charge q2, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is given by:
F = k * |q1| * |q2| / r^2
where F is the force, k is the electrostatic constant (k = 9 x 10^9 Nm^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 the following information:
|q1| = 25 µC = 25 x 10^-6 C
|q| = 8.4 µC = 8.4 x 10^-6 C
F = 27 N
y1 = +0.22 m
y2 = +0.34 m
First, let's determine the distances between the charges.
From the given information, we know that q is at the origin, so its distance from q1 and q2 is simply the y-coordinate of each charge.
r1 = y1 = +0.22 m
r2 = y2 = +0.34 m
Now we can substitute these values into Coulomb's Law equation and solve for |q2|.
27 N = (9 x 10^9 Nm^2/C^2) * (25 x 10^-6 C) * |q2| / (0.34 m)^2
Simplifying:
27 N = (9 x 10^9 Nm^2/C^2) * (25 x 10^-6 C) * |q2| / 0.1156 m^2
Multiply both sides by 0.1156 to isolate |q2|:
3.1196 = (9 x 10^9 Nm^2/C^2) * (25 x 10^-6 C) * |q2|
Divide both sides by (9 x 10^9 Nm^2/C^2) * (25 x 10^-6 C) to solve for |q2|:
|q2| = 3.1196 / [(9 x 10^9 Nm^2/C^2) * (25 x 10^-6 C)]
Calculating:
|q2| = 1.386 x 10^-6 C
Therefore, the magnitude of the charge q2 is 1.386 µC.
To find the magnitude of charge q2, we can first calculate the individual electrostatic forces between the charges and then use the given information about the net force.
The formula to calculate the electrostatic force between two point charges is given by Coulomb's Law:
F = k * |q1| * |q2| / r^2
where F is the force, k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Let's calculate the individual forces:
1. The force between q and q1:
F1 = k * |q| * |q1| / r1^2
Given that the force F1 has a magnitude of 27 N, we can set up the equation:
27 = k * |8.4 × 10^(-6)| * |−25 × 10^(-6)| / (0.22)^2
Simplifying and solving the equation will give us the value of |q1|.
2. Similarly, we can calculate the force between q and q2:
F2 = k * |q| * |q2| / r2^2
Given that the force F2 has a magnitude of 27 N, we can set up the equation:
27 = k * |8.4 × 10^(-6)| * |q2| / (0.34)^2
Simplifying and solving the equation will give us the value of |q2|.
Now that we have the magnitude of |q2|, we can provide the answer to the question.