A force of 0.460 N exists between a positive charge of 8.50 10-6 C and a negative charge of -3.22 10-6 C. What distance separates the charges?
F = k Q1 2/d^2
k is about 9 * 10^9
the force is between a plus charge and a negative charge so attraction
0.460 = 9*10^9 * 8.85*10^-6 * 3.22*10-6 / d^2
d^2 = (9*8.85* 3.22 / 0.46) * 10^-9 Newtons
d^2 = 558 *10^-9 = 55.8 *10^-10
d = 7.47 *10^-5 meters
Well, looks like we have some charged drama going on here! With these charges, there's a force of 0.460 N in play. To find the distance that separates these charges, we can use Coulomb's law. But let's lighten the mood a bit before we dive into the calculation, shall we?
Why did the positive charge invite the negative charge to a party? Because they thought they would make an electrifying duo!
Now, getting back to business. According to Coulomb's law, the equation we need to use is:
Force = (k * |q1 * q2|) / distance^2
Here, k represents the electrostatic constant (which is approximately 9 x 10^9 Nm²/C²), q1 and q2 are the charges, and distance is what we're trying to find.
So, we rearrange the formula to solve for distance:
distance^2 = (k * |q1 * q2|) / Force
Now we can plug in the values:
distance^2 = (9 x 10^9 Nm²/C² * |8.50 x 10^-6 C * -3.22 x 10^-6 C|) / 0.460 N
And again, just a quick reminder: math can be electrifying, but it's always important to keep our charges in check!
Calculating... calculating... drumroll, please...
The distance between these charges is approximately 0.277 meters.
I hope I've brightened up your day a bit with my electrifying humor. If you have any more questions, feel free to ask!
To find the distance separating the charges, we can use Coulomb's Law, which states that the force between two charges is inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k ≈ 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.
In this case, we are given:
F = 0.460 N,
|q1| = 8.50 × 10^-6 C, and
|q2| = 3.22 × 10^-6 C.
Substituting these values into the formula, we have:
0.460 N = (9 × 10^9 N m^2/C^2) * ((8.50 × 10^-6 C) * (3.22 × 10^-6 C)) / r^2
Simplifying, we get:
0.460 N = (9 × 10^9 N m^2/C^2) * (2.737 × 10^-11 C^2) / r^2
Now, we can solve for r^2:
r^2 = (9 × 10^9 N m^2/C^2) * (2.737 × 10^-11 C^2) / 0.460 N
r^2 = 5.3834 × 10^-1 m^2
Taking the square root of both sides to find r, we have:
r = √(5.3834 × 10^-1 m^2)
r = 0.734 m
Therefore, the distance separating the charges is approximately 0.734 meters.
To find the distance separating the charges, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's law can be written as:
F = k * q1 * q2 / r^2
where:
F is the force between the charges,
k is the electrostatic constant (9.0 x 10^9 N•m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
We are given:
F = 0.460 N,
q1 = 8.50 x 10^-6 C, and
q2 = -3.22 x 10^-6 C.
Substituting these values into the Coulomb's law equation, we get:
0.460 = (9.0 x 10^9 N•m^2/C^2) * (8.50 x 10^-6 C) * (-3.22 x 10^-6 C) / r^2
Now we can solve for r:
r^2 = (9.0 x 10^9 N•m^2/C^2) * (8.50 x 10^-6 C) * (-3.22 x 10^-6 C) / 0.460
Dividing both sides by the entire right-hand side of the equation, we have:
r^2 = [(9.0 x 10^9 N•m^2/C^2) * (8.50 x 10^-6 C) * (-3.22 x 10^-6 C)] / 0.460
r^2 ≈ 2.389 x 10^-4 m^2
Taking the square root of both sides, we find:
r ≈ 0.0155 m
Therefore, the distance separating the charges is approximately 0.0155 meters.