An equilateral triangle has sides of 0.14 m. Charges of -9.2, +8.0, and +1.5 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 1.5-µC charge.
Add the two Coulomb forces acting on the 1.5 uC charge, treating them as vectors.
To find the magnitude of the net electrostatic force exerted on the 1.5-µC charge, we can use Coulomb's Law. Coulomb's Law states that the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for the electrostatic force between two charges q₁ and q₂ is given by:
F = k * (|q₁| * |q₂|) / r²
Where:
F is the magnitude of the electrostatic force
k is the electrostatic constant, which is approximately equal to 8.99 x 10^9 N m²/C²
|q₁| and |q₂| are the magnitudes of the charges
r is the distance between the charges
In this case, we have three charges at the corners of an equilateral triangle. Let's label the charges as follows:
q₁ = -9.2 µC
q₂ = 8.0 µC
q₃ = 1.5 µC
The distance between the charges is equal for all three sides of the equilateral triangle, which is given as 0.14 m.
To find the net electrostatic force on the 1.5 µC charge, we need to calculate the individual forces between the 1.5 µC charge and each of the other charges, and then find the vector sum of those forces.
Let's calculate the force between the 1.5 µC and -9.2 µC charges:
|q₁| = |-9.2 µC| = 9.2 µC
r₁ = 0.14 m
Using Coulomb's Law, we can calculate the force between the charges:
F₁ = (k * |q₁| * |q₃|) / r₁²
Now, let's calculate the force between the 1.5 µC and +8.0 µC charges:
|q₂| = |8.0 µC| = 8.0 µC
r₂ = 0.14 m
F₂ = (k * |q₂| * |q₃|) / r₂²
Finally, we can find the net force on the 1.5 µC charge by calculating the vector sum of the individual forces:
Net force = F₁ + F₂
Substituting the given values and performing the calculations will give us the magnitude of the net electrostatic force exerted on the 1.5 µC charge.