Electrostatics - Can someone tell me where I went wrong?

[Eashan1337]

Question: Two small spheres, each having a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. find the charge on each spheres.

 

What I have done:

Given, m = 20 g

distance between the balls = 0.04 m

length of strings = 0.4 m

 

After making a free body diagram, I got two equations.

 

Tcosθ = F (electrostatic force)

Tsinθ = mg

 

Dividing the two, tanθ = mg/F - (i)

 

Now, looking at the triangle made in the figure, I dropped a perpendicular from the vertex from where the two strings are joined.

Looking at the new right angled triangle, I found the length of the perpendicular. It comes out to be 0.3994.

So, tanθ = 0.3994/0.02 = 19.97

 

Now looking at the equation (i), I put the value of tanθ.

 

Therefore, F = mg/19.97.

I'm taking g = 10m/s²

 

F = 10(20)/19.97

F= 10.015

 

(9 x 10⁹ x Q²)/0.0016 = 10.015

 

Q² = 1.78 x 10⁻¹²

 

Q = 1.334 x 10⁻⁶

 

Well, that's what my answer comes, but it's wrong. Can someone guide me where I got it wrong?

[robomont]

since this thread has math it will be split into the math thread and since its speculative it will be split into speculative and so on until you are so confused and the mods feel smart.

 

the charge will be equal but the diameter of mass can make a differenc.the charge cannot be found because the mass has to be in an electric field and there is no reference to what that electric field is.im not a physicist so i may be wrong.

Edited June 2, 2013 by robomont

[ydoaPs]

since this thread has math it will be split into the math thread and since its speculative it will be split into speculative and so on until you are so confused and the mods feel smart.

Excuse me?

the charge will be equal but the diameter of mass can make a differenc.the charge cannot be found because the mass has to be in an electric field and there is no reference to what that electric field is.im not a physicist so i may be wrong.

The balls are charged; they provide the field. You know the mass which gives the gravity and you know all the sides which gives the angles. You just need to figure out the individual forces when the electrostatic force cancels the gravitational force when they're 4cm apart. From there it's just F=ma and basic electrostatics.

[robomont]

couldnt the charge be more inside a higher gradient field?or does it always stay the same regardless?doesnt the diameter of the spheres change the equation?

[swansont]

couldnt the charge be more inside a higher gradient field?or does it always stay the same regardless?doesnt the diameter of the spheres change the equation?

 

"small spheres" is HW question slang for "the size may be ignored". IOW, no matter the answer, the size of the sphere is small compared to the separation distance, so you can treat it like a point.

[daniton]

You just need to figure out the individual forces when the electrostatic force cancels the gravitational force when they're 4cm apart. From there it's just F=ma and basic electrostatics.

Electrostatic force doesn't cancels the gravitational force(and it couldn't cancel ) the tension does.

[ydoaPs]

Electrostatic force doesn't cancels the gravitational force(and it couldn't cancel ) the tension does.

Good catch. +reps