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)
Unfortunately two sides do not determine a triangle. You're going to need an angle or the third side to do this one.
To find the net electric force on q3, we need to consider the individual forces that q1 and q2 exert on q3 and then find the vector sum of these forces.
The electric force between two point charges is given by Coulomb's Law:
F = k * (|q1| * |q2|) / r^2 * r̂
Where:
- F is the magnitude of the electric force,
- k is the electrostatic constant (k = 9.0 x 10^9 N m^2/C^2),
- |q1| and |q2| are the magnitudes of the charges,
- r is the distance between the charges, and
- r̂ is the unit vector pointing from q1 to q2.
Let's calculate the electric forces between q1 and q3, and q2 and q3:
1) Electric force between q1 and q3 (F13):
- q1 = +4.0 x 10^-9 C
- q3 = +5.0 x 10^-9 C
- r13 = 9 m
F13 = k * (|q1| * |q3|) / r13^2 * r13̂
Since the charges are both positive, the electric force between them will be repulsive. Therefore, the direction of F13 will be in the opposite direction of r13.
2) Electric force between q2 and q3 (F23):
- q2 = -2.5 x 10^-9 C
- q3 = +5.0 x 10^-9 C
- r23 = 6 m
F23 = k * (|q2| * |q3|) / r23^2 * r23̂
Since q2 is negative and q3 is positive, the electric force between them will be attractive. Therefore, the direction of F23 will be in the direction of r23.
Once we have calculated F13 and F23, we can find the net electric force on q3 by adding these two vectors together:
Fnet = F13 + F23
To find the components Fnet, x and Fnet, y of the net electric force on q3, we can break down the forces F13 and F23 into their x and y components using trigonometry.
Fnet, x = F13, x + F23, x
Fnet, y = F13, y + F23, y
Finally, we can substitute the values into the formulas and calculate the net electric force on q3:
Fnet, x = F13, x + F23, x
Fnet, y = F13, y + F23, y
Therefore, we need to calculate F13, F23, Fnet, x, and Fnet, y using the above explanations and formulas.