Electric Forces on Point Charge q in Triangle ABC

In summary, the force acting on the charge q can be calculated using Coulomb's Law, and the angle between the direction of this force and the side AB of the triangle can be found using trigonometry.
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Homework Statement


Point charges Q, -2Q and 3Q are situated at the corners A, B and C respectively of an eqilateral triangle of side l, and another point charge q, of the same sign as Q, is placed at the centre of this triangle. What is the force acting on the charge q, and what is the angle between the direction of this force and the side AB of the triangle?

Homework Equations


The Attempt at a Solution


I know that when you have a point charge experiencing forces as a result of several other point charges (electric fields), you resolve the vector forces geometrically and the resultant gives you the direction &magnitude of the resultant force, but what happens when the charge under investigation doesn't lie in line with the other charges? When i resolve the forces using x and y axes at 000degrees and 090degrees, centre being at the location of charge q i get the wrong answer. I'm stuck from there.
 
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Hello, thank you for your question. The force acting on the charge q can be found using Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, the force can be calculated using the following equation:

F = k * (q * Q) / r^2

Where k is the Coulomb's constant, q and Q are the charges of the two point charges, and r is the distance between them.

To find the angle between the direction of this force and the side AB of the triangle, you can use trigonometry. The force will act along the line connecting the center of the triangle (where the charge q is located) and the point charge Q at corner A. This line will form an angle with the side AB of the triangle, which can be found using the following equation:

tanθ = opposite/adjacent = (l/2) / (√3 * l/2) = 1/√3

Where θ is the angle between the direction of the force and the side AB of the triangle.

I hope this helps. Please let me know if you have any further questions.
 

1. What is the formula for calculating the electric force on a point charge in a triangle?

The formula for calculating the electric force on a point charge q in a triangle ABC is F = k*q*(q1/r1^2 + q2/r2^2 + q3/r3^2), where k is the Coulomb's constant, q1, q2, and q3 are the charges of the three vertices of the triangle, and r1, r2, and r3 are the distances from the point charge q to each vertex.

2. How do the positions and charges of the vertices affect the electric force on the point charge?

The positions and charges of the vertices affect the electric force on the point charge by determining the magnitude and direction of the force. The closer a vertex is to the point charge, the stronger the force will be, and the direction of the force will depend on the relative positions and charges of the vertices.

3. Can the electric force on a point charge in a triangle ever be zero?

Yes, the electric force on a point charge in a triangle can be zero if the net charge of the triangle is zero and the point charge is located at the center of the triangle. In this case, the forces from each vertex will cancel each other out, resulting in a net force of zero.

4. How is the electric force on a point charge in a triangle affected by the distance between the charge and the triangle?

The electric force on a point charge in a triangle is inversely proportional to the square of the distance between the charge and the triangle. This means that as the distance increases, the force decreases. However, the relative positions and charges of the vertices will also play a role in determining the final force on the point charge.

5. Can the electric force on a point charge in a triangle be negative?

Yes, the electric force on a point charge in a triangle can be negative. This would occur if the net charge of the triangle is negative and the point charge is located in a position where the forces from the vertices are all pointing in the opposite direction. The force would then be negative, indicating that the charge is being repelled by the triangle.

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