Static electricity problem

moss1234

At what point between a charge of +10uC and a charge of +5uC is the electric field strength zero if the charges are 1 m apart?

finality

You need these two formulas

F=(q1)(q2)/(4(pi)(epsilon)(d^2)

E=F/q

Sub the top equation into the bottom one to cancel the q1s - now you're just left with an expression for E with only one charge.

You need to find the strength of the electric fields created by both charges, and you're looking for the point where, when you subtract one from the other, you get 0. (This is because when a +1C charge is placed between them, they will push it in opposite directions. You need the point where one push cancels out the other. Let's call this point P).

So E1-E2=0
E1=E2

Then you'll need the distances between each charge and the point P expressed in a way so that you only have one variable. You know the two charges are 1m apart, so you can say the distance between the 10microC charge and P is X, and the distance between the 5microC charge and P is (1-X). A diagram helps with this.

Then sub in your values into the E1=E2 equation (lots of things will cancel out) and you'll end up with

10/(x^2) = 5/(1-x)^2

This leads to a quadratic

x^2 - 4x +2 = 0

You'll need to use the quadratic formula to solve this, and you'll end up with 2 values for x. You can discard the one that's greater than 1 as that would be out past one of the charges (there'll be a point out past the 5microC charge where the net charge will equal 0 too,but you're looking for the point between them).

And the other value will be your answer

moss1234

Thanks a million i got an answer of 0.585 but at the back of the book the answer is 0.4142 , strange thanks again (:

finality

moss1234 wrote: »

Thanks a million i got an answer of 0.585 but at the back of the book the answer is 0.4142 , strange thanks again (:

That's 0.4142 away from the 5microC, and it's 0.585 away from the 10microC. :P

moss1234

ahh silly me, thanks again