A +'ve charge Q is fixed to the origin. A -'ve charge 9Q

[abm77]

Homework Statement

A positive charge Q is fixed to the origin. A negative charge with magnitude 9Q is fixed along the positive x-axis a distance d to the right of the origin. Determine a point where a small positive test charge q will experience zero electrical force from the two charges, or show that there is no such point. Draw diagrams to help you.

Homework Equations

[/B]
F_E = kq₁q₂ / r²

The Attempt at a Solution

(+Q)--------d---------(-9Q)

I know the test charge must be to the left of the positive charge Q, and I tried to solve by rearranging the equation to solve to r, but that leaves you with dividing the force, which in this case is zero which does not work.

r = √kq₁q₂ / F_E
But F_E = 0 so this does not work.

 

[CWatters]

Your equation is for the force between two charges. There are three in the problem. The net force must sum to zero not the two individual forces.

 

[abm77]

Your equation is for the force between two charges. There are three in the problem. The net force must sum to zero not the two individual forces.

So would the equation for three charges just include a q₃ at the end? Thus making the small positive test charge 8Q to have it equal zero?

 

[CWatters]

So would the equation for three charges just include a q3 at the end?

Not sure I follow that.

The test charge q is +ve so there are two forces on it..

1) A repulsive force between +Q an +q
2) An attractive force between -9Q and +q

The question asks where must +q be for these two forces sum to zero. Have you studied vector addition?

 

[abm77]

Not sure I follow that.

The test charge q is +ve so there are two forces on it..

1) A repulsive force between +Q an +q
2) An attractive force between -9Q and +q

The question asks where must +q be for these two forces sum to zero. Have you studied vector addition?

How would vector addition work for this question as there are no values for the variables?

 

[Nathanael]

How would vector addition work for this question as there are no values for the variables?

The values are irrelevant, only the relative size of the charges is important (and you know that one has 9 times more charge than the other).

Place the test charge at an arbitrary position on the x-axis, then write an equation for F₁ the force on the test charge from the one charge and another equation for F₂ the force on the test charge from the other charge. The net force is F₁+F₂. The problem asks you to find where this net force is zero.