Calculating Electric Force: Coulomb's Law Example and Solution

[deldel]

Homework Statement

Two identical conducting spheres of charges 3q and -q attract each other with a force of 36 x 10^-3N. When they are separated by a distance of 0.2 m. The spheres are brought into contact with each other and then separated by a distance of 0.1 m.

What is the magnitude of the electric force on each one exerts on the other?

Homework Equations

The Attempt at a Solution

I just need to make sure that i can get Q₁ and Q₂ correctly[/B]

So what i tried to do was rearrange the formula to fit the question by doing
Q₁ x Q₂ = k x f / d²

so, 9x10⁹ x 36 x 10^-3
(0.2)²

= 324 x 10⁶
(2 x 10^-1)²

= 324 x 10⁸
2

= 162 x 10⁸

so Q₁ = 162 and Q₂ is -54

I think its wrong, please can anyone check

 

[gneill]

So what i tried to do was rearrange the formula to fit the question by doing
Q₁ x Q₂ = k x f / d²

That rearrangement is not correct. Show your steps.

 

[deldel]

What is the formula to find Q₁ and Q₂

how should i properly arrange it?

 

[gneill]

What is the formula to find Q₁ and Q₂

how should i properly arrange it?

What formula did you begin with? It should be elementary algebra to rearrange it. So show your steps.

 

[deldel]

i began with F = K x Q₁ x Q₂ / d²


since the force is given but the charges were not, i tried to swap them, resulting in

Q₁ x Q₂ = K x F / d²


but it was incorrect

 

[gneill]

i began with F = K x Q₁ x Q₂ / d²


since the force is given but the charges were not, i tried to swap them, resulting in

Q₁ x Q₂ = K x F / d²


but it was incorrect

It's incorrect because your algebra is incorrect.

You can't just "swap" variables from one side to the other. Operations must be performed identically on each side of an equation to accomplish what you want.

Start again with the original equation. As a first step, multiply both sides by d².

 

[deldel]

Alright, Thank you sir.

 

[mfb]

In addition, it is useful to keep the units in the equations. You would have noted the problem then because the units do not match any more.