Two point charges that have charge values of 4.0 X 10^-6 C and -8.0 X 10^-6 C, respectively, are separated by 2.4 X 10^-2 m. What is the mutual force between them, given that kC = 8.99 X 10^9 Nm^2/C^2?
I got the Felectric as -5.0 X 10^2 N, but I'm not sure if that value is supposed to be negative.
8.99*10^9[-32*10^-12 / 5.76*10^-4]
= -49.9 *10^1
= -500 agree
force is attractive (opposite signs). I guess you could call that negative.
Well, well, well. A negative charge and a positive charge walk into a bar. The bartender says, "Hey, why the long face?" The positive charge replies, "I'm feeling a bit negative today."
Now, let's talk about the force between those charges. The formula we need here is Coulomb's Law, which states that the force between two charges is given by:
Felectric = k * (q1 * q2) / r^2
where:
- Felectric is the electric force between the charges,
- k is the electrostatic constant (kC in this case),
- q1 and q2 are the charges, and
- r is the distance between the charges.
Now let's calculate. Plugging in the values you provided:
Felectric = (8.99 X 10^9 Nm^2/C^2) * ((4.0 X 10^-6 C) * (-8.0 X 10^-6 C)) / (2.4 X 10^-2 m)^2
Doing the math, we get:
Felectric = -480 N
So, the mutual force between these charges is indeed -480 N, which means they repel each other. It's negative because the charges have opposite signs. It's like when you try to push away someone who's standing on your foot. They wouldn't like that, would they?
To calculate the mutual force between two point charges, you can use Coulomb's Law:
Felectric = kC * (|q1| * |q2|) / r^2
Where:
- Felectric is the mutual force between the charges in Newtons (N)
- kC is the Coulomb's Constant, equal to 8.99 x 10^9 Nm^2/C^2
- |q1| and |q2| are the magnitudes of the charges in Coulombs (C)
- r is the separation distance between the charges in meters (m)
Let's plug in the given values:
|q1| = 4.0 x 10^-6 C
|q2| = -8.0 x 10^-6 C (Note that the charge is negative because it has an opposite sign to |q1|)
r = 2.4 x 10^-2 m
Substituting these values into the formula:
Felectric = (8.99 x 10^9 Nm^2/C^2) * (4.0 x 10^-6 C) * (-8.0 x 10^-6 C) / (2.4 x 10^-2 m)^2
Calculating this expression, we get:
Felectric = -5.99 N
Since the result is negative, it indicates that the charges exert an attractive force on each other.
To calculate the mutual force between two point charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the magnitude of the 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 is the mutual force between the charges,
- k is the electrostatic constant, 8.99 x 10^9 Nm^2/C^2,
- q1 and q2 are the charges of the two point charges, and
- r is the distance between the charges.
In this case, we have two point charges:
q1 = 4.0 x 10^-6 C (positive charge)
q2 = -8.0 x 10^-6 C (negative charge)
The distance between them is:
r = 2.4 x 10^-2 m
Substituting these values into the equation, we have:
F = (8.99 x 10^9 Nm^2/C^2) * (|4.0 x 10^-6 C| * |-8.0 x 10^-6 C|) / (2.4 x 10^-2 m)^2
Calculating this expression should yield the value for the mutual force between the two charges.