If one point charge is located at each corners of a right triangle, where q1=q3= 5.0μC, q2= 2.0 μC, and a= 0.10 m. Find the resultant force felt by the third charge
To find the resultant force felt by the third charge, we can calculate the individual forces exerted by the other two charges on it, and then add them vectorially.
The magnitude of the force between two point charges can be calculated using Coulomb's law:
F = (k * |q₁ * q₂|) / r²
Where:
- F is the force between the two charges.
- k is Coulomb's constant, approximately equal to 9 x 10^9 N m²/C².
- q₁ and q₂ are the magnitudes of the charges.
- r is the distance between the charges.
Let's start by calculating the force exerted by charge q₁ on the third charge.
First, find the distance (r₁) between q₁ and the third charge. In this case, the distance is the length of one of the sides of the right triangle, which is given as a = 0.10 m.
Next, calculate the force (F₁) using Coulomb's law:
F₁ = (k * |q₁ * q₃|) / r₁²
Substitute the known values: q₁ = q₃ = 5.0 μC, and r₁ = a = 0.10 m. Remember to convert the charges to coulombs (1 μC = 1 x 10^-6 C).
Calculate F₁ using the given values.
Now, repeat the same process to calculate the force (F₂) exerted by charge q₂ on the third charge.
The distance (r₂) between q₂ and the third charge can be found using the Pythagorean theorem:
r₂ = √(a² + a²) = √2a²
Then, calculate F₂ using Coulomb's law:
F₂ = (k * |q₂ * q₃|) / r₂²
Substitute the known values: q₂ = 2.0 μC, q₃ = 5.0 μC, and r₂ = √2a². Convert the charges to coulombs if necessary.
Finally, find the resultant force (Fᵣ) by vectorially summing the forces F₁ and F₂. Since both forces act in different directions, we need to use vector addition. Let's call the angle between the two forces θ.
Using the law of cosines, we can find the magnitude of the resultant force:
Fᵣ = √(F₁² + F₂² + 2F₁F₂cosθ)
Therefore, the resultant force felt by the third charge can be calculated using the above steps.