# Electrostatic Force Derivitive

Well,I've tried attempting this problem but I am not sure if I approached it the right way. Here is a link for the diagram and the question.

If anyone could check it over and point out any mistakes and tell me if I make any sense what so ever,then you would make my day.

My solution:

Fe=Fg therefore
qE=mg ------> E=mg/q

x-component: Ex¹= Ecosø
= Fe/q cosø
= mg/q cosø

y-component: Ey¹= Esinø
= Fe/q sinø
= mg/q sinø

E¹= square root of (mg/cosø)² + (mg/sinø)²

Another solution that I thought up of:

Isn't tension just the sum of all forces acting on a object...therefore:

Ft= Fe+Fg
Fe= Fg-Ft
= mgsinø- Ft

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cepheid
Staff Emeritus
Gold Member
a_ng116 said:
Fe=Fg
Just wondering why this very first step??? I didn't see that in the problem, although I could be blind :rofl:

Also, just as an FYI, it should be a 'derivation' in the thread title, since that is the term for arriving at an equation by deriving it. A "derivative" is something else in calculus, and so that confused me initially.

If you explain that first step, I should be able to help further...

As for this question:

a_ng116 said:
Isn't tension just the sum of all forces acting on a object...
I'm afraid that the answer, in general, is no. Tension is just the name given to a force tending to 'stretch' an object, i.e. pull it apart. When referring to some object suspended by a rope, the object pulls on the rope, which pulls back up on the object, keeping it suspended. The rope is taut, not slack, so it is in tension.

Yeah, the first line of your working should be Fe = Ftsin θ.

Also, how are you getting x and y components of the electric field? E is in the direction of Fe and from the diagram, Fe is only in the x direction.

Hmmm...alright.It actually somewhat makes sense. There is only an x-component to the electrostatic force so starting with what nylex suggested Fe=Ftsinø,would it be true then to say that:

Fe=Ft-Fgsinø
= ma- mgsinø

My rationale for this is that earth exerts a downward force F=-mg on the test body correct?So the test body exerts and upward force F=+mg on the earth. The upward force is caused by the tension on the thread holding the test body and this is working against gravity keeping it suspended, hence Ft=ma. Anyways...more feedback would be much appreciated even despite not making much sense before in my previous derivation. And you know, if I'm completly wrong again here.