Coulomb's Law (Electricity and Magnetism) Question

[thepassenger48]

Homework Statement

Five point charges on a straight line are separated by a distance of 0.01 m. For what values of q2 and q4 would the net force on each of the other three charges be zero?

q1-----q2-----q3-----q4-----q5

Where:
q1= 2x10^-6 C
q3= 1x10^-6 C
q5= 2x10^-6 C

Homework Equations

Force = (q1q2K)/r²
Where q are the charges, K is a constant (8.99x10^9) and r is the distance between the charges.
The problem is solved using a free body diagram and a summation of forces.

The Attempt at a Solution

I have no idea as to how to approach this problem, I'm not looking for a full solution but for some advice. My main questions are; how do I deal with the forces and their directions? Then how can I use algebra to optain the values of q2 and q4?
Thanks!

 

[turdferguson]

Sum up the forces for q1, q3, and q5. You shoud have 3 equations and 2 unknowns, because you know the distance each force acts over

 

[m2003]

I would approach this problem by first drawing a free body diagram of the system, as suggested in the homework equations. This will allow me to visualize the forces acting on each charge and their directions.

Next, I would use the formula for Coulomb's Law to calculate the force between each pair of charges. For example, the force between q1 and q2 would be:

F12 = (q1q2K)/r12²

Where r12 is the distance between q1 and q2.

Since we are looking for values of q2 and q4 where the net force on the other three charges is zero, we can set up an equation where the sum of forces on q3, q4, and q5 is equal to zero. This can be written as:

F13 + F23 + F34 + F45 = 0

Substituting in the values for q1, q3, q5, and r, we can solve for q2 and q4.

It is important to note that the direction of the force will depend on the sign of the charges. Positive charges will repel each other, while negative charges will attract. So when solving for q2 and q4, it is important to consider the direction of the forces and ensure that they add up to zero.

In conclusion, to approach this problem, I would use a free body diagram, Coulomb's Law, and algebra to calculate the values of q2 and q4 that would result in a net force of zero on the other three charges.