Electric Force: Equilateral Triangle

In summary: North, and WestIn summary, the problem involves three charges (+Q, +Q, and -Q) placed at the vertices of an equilateral triangle. The task is to find the magnitude and direction of the force on one of the +Q charges. After setting up the triangle and calculating the forces, the net force is determined to be (2QK/s^2) and its direction is given as θ = tan-1 (∑Fy / ∑Fx), which evaluates to 120 degrees. This results in a vector pointing towards the west.
  • #1
Sirmeris
1
0

Homework Statement


Three charges, +Q, +Q, and -Q are placed at the vertices of an equilateral triangle of length "s" on a side. Find the magnitude and direction of the force on one of the +Q charges.


Homework Equations


ForceElectric=(K*q1*q2/d2)


The Attempt at a Solution


I've set the triangle up so that the bottom side is parallel to the x-axis. My +Q charges are in both the bottom left (charge 1) and bottom right (charge 3) corners, while the -Q charge (charge 2) is at the top. Charge 3 is the charge that I have chosen to do the calculation for.

Force2 on 3 = (2QK/s2)

Force2 on 3 = Force1 on 3, so Force1 on 3 = (2QK/s2)

x-component: Forcex:2 on 3 = (2QK/s2)*cos(60°) = (QK/s2)

y-component: Forcey:2 on 3 = (2QK/s2)*sin(60°)



∑Fx = Force1 on 3 - Forcex:2 on 3

∑Fx = (2QK/s2) -(QK/s2)


∑Fy = Forcey:2 on 3

∑Fy = (2QK/s2)*sin(60°)




Fnet = ∑Fy + ∑Fx (vector equation)

Fnet = √((∑Fy)2 + (∑Fx)2)

Simplified this (hopefully) goes to:



Fnet = (2QK/s2)

This was my final answer for the magnitude, but I'm not even sure if it is correct, or if my procedure is right. I'm also not sure how to find the direction. Any help would be greatly appreciated! Thank-you!
 
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  • #2
Hi Sirmeris. Welcome to Physics Forums.

Force2 on 3 = (2QK/s2)
Check your algebra ...

Q x Q = Q2
 
  • #3
Fnet = ∑Fy + ∑Fx (vector equation)
Once you have ∑Fx and ∑Fy you can determine the magnitude using Pythagoras, as you show, and the angle, θ, of that vector is given as

θ = tan-1 (∑Fy / ∑Fx)

Always wise to sketch these, so you can be sure to give your final answer in the correct quadrant.
 
  • #4
Hi Sirmeris
Use this diagram to find net force on +Q.
Net.F=√(F^2+F^2+2F*Fcosθ)
θ=120.In this problem force on +Q due to -Q and other +Q charge is equal.
 
  • #5
Untitled.png
this is the figure.
What should be the direction of the resultant.
 
  • #6
Satvik Pandey said:
View attachment 71444 this is the figure.
What should be the direction of the resultant.
East
 

1. What is electric force?

Electric force is a fundamental force in physics that describes the attraction or repulsion between two charged particles. It is caused by the interaction of electric fields, which are created by charged particles.

2. What is an equilateral triangle?

An equilateral triangle is a type of triangle where all three sides are equal in length and all three angles are equal to 60 degrees.

3. How does electric force relate to an equilateral triangle?

In an equilateral triangle, the three charges at each vertex will experience electric forces that balance each other out due to the symmetry of the triangle. This results in a net force of zero on the charges.

4. Can an equilateral triangle have a non-zero electric force?

Yes, if the equilateral triangle is not symmetrical or if the charges at each vertex are not equal, then there will be a net electric force acting on the charges.

5. How is electric force calculated for an equilateral triangle?

The electric force between two charges in an equilateral triangle can be calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In an equilateral triangle, this distance is equal for all three charges, resulting in a balanced net force.

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