Poteintial difference to move mass

1. Sep 27, 2007

indigojoker

There's a small sphere of mass m that hangs by a thread. the sphere is between two parallel plates L apart. The sphere has a charge Q. What is the potential difference that will make the plates to assume an angel of 20 degrees with the vertical?

$$F=QE=mg \sin \theta$$
$$E=\frac{mg \sin 20}{Q}$$
$$V= - \int _0 ^L \frac{mg \sin 20}{Q}dx$$
$$V= - \frac{mgL \sin 20}{Q}d$$

i feel like this question should involve more work. was my thought process correct?

2. Sep 27, 2007

Avodyne

Yes, it's correct. (But the d in your last line is presumably a typo.) Also, since the question asks for "potential difference", the minus sign is not really relevant.

3. Sep 27, 2007

indigojoker

yes it's a typo

could you explain why the potential difference is not relevant?

4. Sep 27, 2007

Andrew Mason

How do you get the first statement? Do a free body diagram of the forces on the suspended mass. There is the tension in the string, gravity and the electric force. From a free body vector diagram you should be able to get the expression for E and then V (=E/L) .

AM

5. Sep 28, 2007

Andrew Mason

If you do the free body diagram you will see that the gravitational and electric forces have to be balanced by the tension in the string.

$$\vec{T} = q\vec{E} + m\vec{g}$$

This means that:

$$T\sin{20} = qE$$
$$T\cos{20} = mg$$

Dividing:

$$qE/mg = \tan{20}$$

$$EL = V$$, so

$$V = mgL \tan{20}/q$$

AM

Last edited: Sep 28, 2007