Calculating Coulombic Forces on a Particle: A Symmetrical Three-Particle System

In summary, the question asks for the magnitude and direction of the force acting on particle A, which is located on the y-axis at the square root of 3, due to particles B and C, located on the x-axis and separated by 2a. The relevant equations are Coulomb's law and the concept that all forces should be attractive. The resulting force on A should be twice the force from either B or C. To solve, the formula for FAB is (2q2)/4∏ε0rAB rAB hat, where r is the distance between A and B. By using trigonometric ratios, r can be calculated as √(a2+3). Thus, the final formula for F
  • #1
Roodles01
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Homework Statement


I have a simple question about forces on separated particles, but still need a bit of help. I have put down what I can:

3 particles;
A on y-axis @ √3, charge "q"
B & C each on x-axis, symmetrical about origin, separated by 2a, both charge "q".

Find magnitude & direction of force acting on A due to B & C.

Homework Equations


Coulombs law FAB[/SUB] = (q1 q2)/4∏ε0rAB rAB hat
All force should be attractive so
Resultant force on A should be 2x force from either A or B? Yes?
So should now become
FAB = (2 q2)/4∏ε0rAB rAB hat

r, from trig ratios, should be . . . . er . . . . √(a2+3) . . . . . feeling foolish here please helpThen F[/SUB] AB = 2q2 / ∏ε0√(a^2+3)
 
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  • #2
The Attempt at a SolutionI'm not sure if I'm totally wrong, or just missing an easy step. Can anyone help?
 

What is the force on a particle due to Coulomb's law?

The force on a particle due to Coulomb's law is the force of attraction or repulsion between two electrically charged particles. It is given by the equation F = (kQ1Q2) / r2, where k is the Coulomb's constant, Q1 and Q2 are the charges of the particles, and r is the distance between them.

How does the magnitude of the force on a particle change with distance?

The magnitude of the force on a particle due to Coulomb's law decreases as the distance between the two charged particles increases. This relationship is described by the inverse square law, where the force is inversely proportional to the square of the distance between the particles.

Can the force on a particle be negative?

Yes, the force on a particle due to Coulomb's law can be negative. This occurs when the two charged particles have opposite charges, resulting in an attractive force. A positive force indicates repulsion between two particles with the same charge.

What happens to the force on a particle if the charges of the particles are doubled?

If the charges of the particles are doubled, the force on the particle will also double. This is because the force is directly proportional to the charges, as shown in the Coulomb's law equation.

How does the medium between the charged particles affect the force?

The medium between the charged particles can affect the force by changing the value of the Coulomb's constant, which depends on the electrical properties of the medium. In a vacuum, the Coulomb's constant has a value of 8.9875 x 109 Nm2/C2, but in a different medium, it may have a different value, resulting in a different force on the particle.

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