what must be the distance between the point charge q1=260√'C and point charge q2= 470✓`C for the electrostatic force between them to have a magnitude of 5.70N.
pls help.
To determine the distance between point charges q1 and q2 for a given electrostatic force, you can use Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's Law:
F = k * |q1 * q2| / r^2
where:
F is the magnitude of the electrostatic force,
k is the electrostatic constant (k = 8.99 * 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the two point charges, and
r is the distance between the two point charges.
In this case, you have F = 5.70 N, q1 = 260√C = 260 * sqrt(C), q2 = 470✓C = 470 * sqrt(C), and you need to find r.
Rearranging Coulomb's Law to solve for r:
r = √(k * |q1 * q2| / F)
Substituting the given values:
r = √[(8.99 * 10^9 Nm^2/C^2) * |(260√C * 470✓C)| / 5.70 N]
Now let's calculate the value of r:
r = √[(8.99 * 10^9 Nm^2/C^2) * |(260 * sqrt(C) * 470 * sqrt(C))| / 5.70 N]
r = √[(8.99 * 10^9 Nm^2/C^2) * (260 * 470) C]
r = √(8.99 * 10^9 Nm^2/C^2 * 121,220 C)
r = √(8.99 * 10^9 Nm^2 * 121,220)
r = √(1.0905378 * 10^15 Nm^2)
Calculating the square root:
r ≈ 1.045 * 10^8 meters
Therefore, the distance between the point charge q1 = 260√C and the point charge q2 = 470✓C for the electrostatic force between them to have a magnitude of 5.70 N is approximately 1.045 * 10^8 meters.
To find the distance between the point charges q1 and q2 for the electrostatic force to have a magnitude of 5.70N, we can use Coulomb's Law. Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their charges and 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 magnitude of the electrostatic force,
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.
Using the given values: q1 = 260√C, q2 = 470✓`C, and F = 5.70N, we can rearrange the formula to solve for r:
r = √((k * |q1| * |q2|) / F)
Substituting the values into the formula:
r = √((9 × 10^9 N•m^2/C^2) * (260√C * 470✓`C) / 5.70N)
Now, let's simplify the expression:
r = √((9 × 10^9 N•m^2/C^2) * (260 * 470) C)
r = √((9 × 10^9 N•m^2/C^2) * 121,200 C)
r = √(1090800000000 N•m^2/C^2)
Taking the square root:
r ≈ 1.04 × 10^6 m
Therefore, the distance between the point charges q1 and q2 should be approximately 1.04 × 10^6 meters for the electrostatic force to have a magnitude of 5.70N.