We study three point charges at the corners of a triangle. Their charges are q1 = +4.0 10-9 C, q2 = −2.5 ✕ 10−9 C, and q3 = +5.0 10-9 C. Two distances of separation are also given,
ℓ12 = 6 m and ℓ13 = 9 m.
Find the net electric force on q3
1- Fnet, x (N)
2- Fnet, y (N)
I agree you will have to do it in x, y directions.
I will set up the x direction, you can do the y.
F12x=k q3q1/9^2 * (4.5/9)
now notice the last term.That is Sine of the angle between the vertical from 3, and the direction of L13. Notice if the pt 3 had been directly over 1, then the x component would have been zero.
Now when you do the y component, your term will be cosine(arctan4.5/9), and you can convert that to a cosine(arccos xxx) as you know the vertical distance from the pyth theorm.
To find the net electric force on q3, we need to calculate the forces between q3 and q1 and q3 and q2 separately, and then add them vectorially to find the resultant.
The electric force between two point charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the electric force
k is the electrostatic constant (9 × 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance of separation between the charges
Let's calculate the forces between q3 and q1:
F13 = (k * |q3 * q1|) / ℓ13^2
Substituting the given values:
F13 = (9 × 10^9 N m^2/C^2) * (5.0 × 10^-9 C * 4.0 × 10^-9 C) / (9 m)^2
Simplifying this calculation will give us the magnitude of the force between q3 and q1.
Next, let's calculate the force between q3 and q2:
F23 = (k * |q3 * q2|) / ℓ12^2
Substituting the given values:
F23 = (9 × 10^9 N m^2/C^2) * (5.0 × 10^-9 C * 2.5 × 10^-9 C) / (6 m)^2
Again, simplifying this calculation will give us the magnitude of the force between q3 and q2.
Finally, to find the net electric force on q3, we need to add these two forces vectorially. The net force, Fnet, can be calculated using the Pythagorean theorem:
Fnet = √(F13^2 + F23^2)
This will give us the magnitude of the net electric force on q3.
Now, the net electric force can be resolved into its x and y components using the angles and trigonometry. The x-component, Fnet,x, is given by:
Fnet,x = Fnet * cos(θ)
And the y-component, Fnet,y, is given by:
Fnet,y = Fnet * sin(θ)
Where θ is the angle between the resultant force and the x-axis.