A point particle that has a charge of 12.5 µC is located at x = 0, y = 0 and a point particle that has a charge q is located at x = 10.0 cm, y = 0. The electric force on a point particle that has a charge of 5.0 µC at x = 20.0 cm, y = 0 is -(19.7) N . Determine the charge q.
Well, since we're talking about electric forces, let's remember that opposites attract and likes repel, just like in high school. So, in this case, we have the force being negative, so that means our two charges must be of the same sign, otherwise they would repel each other in the positive direction.
Now, let's do some calculations. The formula for electric force between two charges is given by Coulomb's law, which is F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant, q1 and q2 are the two charges, and r is the distance between them.
In this case, the distance is given as 20.0 cm, which is 0.2 meters. And we know that F = -19.7 N. Plugging in these values, we get:
-19.7 N = k * (5.0 µC * q) / (0.2)^2
Now, let's solve for q. But first, let me grab my calculator... I'll be right back!
*Clown Bot turns around and pretends to walk away*
*Clown Bot quickly returns*
Just kidding! I didn't actually go anywhere. Okay, let me do some math here. *Clown Bot mimes pressing buttons on an imaginary calculator*
After some calculations, I find that the charge q is approximately -0.395 µC. So, it turns out our charge q is negative, just like the force! It seems like these two charges really don't get along.
Remember, though, that this is just an approximation. My calculations might have a little bit of clownishness in them, so don't take them too seriously!
To find the charge q of the point particle located at x = 10.0 cm, y = 0, we can apply Coulomb's law.
Coulomb's law states that the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
We are given:
- Charge of the first particle (located at x = 0, y = 0) = 12.5 µC
- Charge of the second particle (located at x = 20.0 cm, y = 0) = 5.0 µC
- Electric force on the second particle = -19.7 N
Using Coulomb's law formula:
F = k * (|q1| * |q2|) / r^2
where F is the electric force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
We can rewrite the formula as:
q2 = (F * r^2) / (k * |q1|)
Now let's substitute the known values into the equation:
- F = -19.7 N
- r = 20.0 cm = 0.2 m
- k = 8.99 * 10^9 Nm^2/C^2
- q1 = 12.5 µC = 12.5 * 10^-6 C
Substituting these values, we get:
q2 = (-19.7 N * (0.2 m)^2) / (8.99 * 10^9 Nm^2/C^2 * 12.5 * 10^-6 C)
Calculating this expression gives us:
q2 ≈ -0.08779 C
Therefore, the charge q of the point particle located at x = 10.0 cm, y = 0 is approximately -0.08779 C.
To determine the charge q of the particle located at x = 10.0 cm, y = 0, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two point charges is given by the equation:
F = k * (|q1 * q2| / r^2)
Where F is the electric force between the charges, k is the electrostatic constant (9.0 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:
- Charge of the first particle (located at x = 0, y = 0): q1 = 12.5 µC = 12.5 x 10^-6 C
- Charge of the second particle (located at x = 10.0 cm, y = 0): q2 = q
- Distance between the first and second particles: r = 10.0 cm = 0.1 m
The electric force on the third particle (located at x = 20.0 cm, y = 0) is given as -19.7 N. Since we know that like charges repel each other, the negative sign indicates that the forces on the third particle and the second particle are in opposite directions.
Using Coulomb's Law and the given information, we can set up the equation:
F = k * (|q1 * q2| / r^2)
-19.7 N = (9.0 x 10^9 Nm^2/C^2) * (|5.0 x 10^-6 C| * |q| / (0.1 m)^2)
Simplifying the equation, we can isolate the unknown charge q:
|q| = (|F| * (0.1 m)^2) / (9.0 x 10^9 Nm^2/C^2 * |5.0 x 10^-6 C|)
|q| = (19.7 N * (0.01 m^2)) / (4.5 x 10^3 Nm^2/C)
|q| ≈ 4.37 x 10^-5 C
Since the magnitude of the charge cannot be negative, the value of q is approximately 4.37 x 10^-5 C.