Question

In: Physics

Three particles are fixed on an x axis. Particle 1 of charge q1 is at x...

Three particles are fixed on an x axis. Particle 1 of charge q₁ is at x = -a and particle 2 of charge q₂ is at x = +a. If their net electrostatic force on particle 3 of charge Q is to be zero, what must be the ratio q₁/q₂ when particle 3 is at (a) x = +0.754a and (b) x = +1.65a?

Expert Solution

To start with we are considering that the charge Q is at location x from the origin. The force on Q due to charge q1 located at x=-a is F1 and can be calculated as

Both are positively charges so they will repel each other so the direction of the force is towards the +x axis.

The force on Q due to charge q2 located at x=+a is F2 and can be calculated as

Again both are positively charged so they will repel each other so force will be along -x axis or in the backward direction.

these two forces are in opposite direction so the resultant force on Q charge is

It has to be zero so

(a) If x=+0.754 a then

The ratio of the charges q1/q2=50.84

(b) When x=+1.65 a then the force on Q due to q1 and q2 will be in the same directions and will be directed forward so in this case the net force F_R will be

The resultant force has to be zero so

Putting x=+1.65 a in the above we get

The ratio of the charges in this case q1/q2=-16.62

genius_generous answered 4 months ago

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