What Potential Difference Between Plates Causes a 30° Thread Angle?

[ovoleg]

Can anyone help me with a hint of some sort? I am lost...

A small sphere with mass 1.50 g hangs by a thread between two parallel vertical plates 5.00 cm apart. The plates are insulating and have uniform surface charge densities + and -. The charge on the sphere is q = 8.90 10-6 C. What potential difference between the plates will cause the thread to assume an angle of 30.0° with the vertical

 

[ovoleg]

I know the field between two charged plates is E=sigma/epsilon_0...

The way I think of it is that I need to find the forces acting on it and then have that be my E value and then integrate E through distance 5cm?

This is what I tried but I did not get 47.7V

kq*cos30*.015kg*.05=51.95V

 

[Curious3141]

a) What is the definition of the electric field in terms of voltage (potential difference) and distance ? There is a simple formula, check your text or notes.

b) What is the relationship between the force on a charged body, the quantity of charge on that body and the electric field strength the body is subjected to ?

c) Draw a force diagram. What are the forces acting on the ball, and how do they resolve horizontally and vertically ?

d) Put it all together (in symbols), rearrange to form an expression for V, the voltage, then plug in values to get the answer.

 

[ovoleg]

a) What is the definition of the electric field in terms of voltage (potential difference) and distance ? There is a simple formula, check your text or notes.

b) What is the relationship between the force on a charged body, the quantity of charge on that body and the electric field strength the body is subjected to ?

c) Draw a force diagram. What are the forces acting on the ball, and how do they resolve horizontally and vertically ?

d) Put it all together (in symbols), rearrange to form an expression for V, the voltage, then plug in values to get the answer.

a) E=Vab/d
b) E = F/q

c)F=(mg)*cos(30)?

d) Vab=(mg)*cos(30)*d/q?

I get 71.52007V

:(

Please help :) I've been trying for the past few hours

 

[durt]

Should be tan(30) right? Draw the force diagram again. Other than that, I think you've got it.

 

[ovoleg]

Should be tan(30) right? Draw the force diagram again. Other than that, I think you've got it.

'
THANKS!

 

[Curious3141]

a) E=Vab/d
b) E = F/q

Those two are fine.

c)F=(mg)*cos(30)?

No. OK, the sphere is in equilibrium right ? So there is no net force on i, all the forces balance. What are these forces ?

Let's list them :

1) Weight = mg, acts vertically downward.
2) Tension in the suspending string, call it T, acts upward in the direction of the string (at the 30 degree angle it is hanging at).
3) Electrostatic force, call it F = qE = qV/d, where q is the charge and E the electric field strength, V is the voltage and d is the distance between the plates. Acts horizontally to the right.

The easiest thing to do now is to resolve the forces horizontally and vertically and set up equations.

Basic concept : Vertical component of tension exactly balances the weight.
Horizontal component of tension exactly balances the electrostatic force.

You can get two equations with two unknowns, T and V. You need to solve for V so eliminate T. Now get an expression for V.

d) Vab=(mg)*cos(30)*d/q?

Not correct, I'm afraid. Hopefully, you can get it now. Don't forget to specify which plate is positively charged, left or right. Remember the ball is positively charged, according to the question.

 

[Curious3141]

Should be tan(30) right? Draw the force diagram again. Other than that, I think you've got it.

Hold on, I think it's important he gets this conceptually instead of just trying out different trig ratios.