A charge of -3.10 nC and a charge of -6.65 nC are separated by a distance of 80.0 cm. Find the position at which a third charge of +7.10 nC can be placed so that the net electrostatic force on it is zero.
To find the position at which the net electrostatic force on the third charge is zero, we need to consider the forces between each pair of charges.
The force between two charges can be calculated using Coulomb's Law:
F = (k * q₁ * q₂) / r²
Where:
F is the electrostatic force
k is Coulomb's constant (9 × 10^9 N m²/C²)
q₁ and q₂ are the charges
r is the distance between the charges
Let's calculate the forces between the third charge and the two charges:
For the first pair (third charge and charge of -3.10 nC):
F₁ = (k * q₁ * q₂) / r²
F₁ = (9 × 10^9 N m²/C²) * (7.10 × 10^(-9) C) * (-3.10 × 10^(-9) C) / (0.80 m)²
For the second pair (third charge and charge of -6.65 nC):
F₂ = (k * q₁ * q₂) / r²
F₂ = (9 × 10^9 N m²/C²) * (7.10 × 10^(-9) C) * (-6.65 × 10^(-9) C) / (0.80 m)²
Since we want the net force to be zero, the magnitudes of these forces must be equal:
|F₁| = |F₂|
Solving for the position (r), we can rewrite the equation as:
(r₁/r₂) = sqrt(|q₁/q₂|)
Where:
r₁ is the distance between the third charge and the charge of -3.10 nC
r₂ is the distance between the third charge and the charge of -6.65 nC
Now, let's substitute the given values into the equation and solve for r₁:
(r₁/0.80) = √(|7.10/3.10|)
(r₁/0.80) = √(2.29)
(r₁/0.80) = 1.513
Solving for r₁:
r₁ = 1.513 * 0.80
r₁ = 1.2104 m
Therefore, the position at which the net electrostatic force on the third charge of +7.10 nC is zero is approximately 1.2104 meters away from the charge of -3.10 nC.
To find the position at which a third charge can be placed so that the net electrostatic force on it is zero, we can apply the principle of electrostatic equilibrium. In this case, we have two charges, one positive and one negative, and we need to find the position where the net force on a third charge is zero.
The electrostatic force between two charges can be calculated using Coulomb's Law:
F = k * |q1 * q2| / r^2
Where F is the electrostatic force, k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the two charges, and r is the distance between the charges.
First, let's find the electrostatic force between the two given charges.
F1 = k * |(-3.10 nC) * (-6.65 nC)| / (0.80 m)^2
To find the net force on the third charge, we need to consider the fact that the force between the third charge and each of the other charges should be equal in magnitude but opposite in direction.
Let the distance between the third charge and the first charge be x, and the distance between the third charge and the second charge be (0.80 m - x) since the total distance between the two charges is 0.80 m.
Then, the net force on the third charge can be expressed as the sum of the forces between the third charge and each of the other charges.
Net force = F3-1 + F3-2
Using Coulomb's Law, we can write:
F3-1 = k * |(7.10 nC) * (-3.10 nC)| / (x)^2
F3-2 = k * |(7.10 nC) * (-6.65 nC)| / (0.80 m - x)^2
To find the position where the net force is zero, we need to set the magnitude of F3-1 equal to the magnitude of F3-2, and solve for x:
k * |(7.10 nC) * (-3.10 nC)| / (x)^2 = k * |(7.10 nC) * (-6.65 nC)| / (0.80 m - x)^2
Simplifying and solving for x will give us the position where the net electrostatic force on the third charge is zero.