# Opposite Charged Plates with Sphere

## Homework Statement

A small sphere with mass 2.90 g hangs by a thread between two large parallel vertical plates 0.05 m apart. The plates are insulating and have uniform surface charge densities + \sigma and - \sigma . The charge on the sphere is q = 9.70×10^6 C.

What potential difference between the plates will cause the thread to assume an angle of 30.0 deg with the vertical

## Homework Equations

$$Delta(V) = Ed = \frac {F_{elec} * d} {q} = \frac {(mg)*(d)*tan(30)} {q}$$

## The Attempt at a Solution

$$\frac {(2.90*8.90)*(0.05)*tan(30)} {9.70*10^{-6}}$$

The online program complains that its wrong, I'm wondering is the equation correct?

## Homework Statement

A small sphere with mass 2.90 g hangs by a thread between two large parallel vertical plates 0.05 m apart. The plates are insulating and have uniform surface charge densities + \sigma and - \sigma . The charge on the sphere is q = 9.70×10^6 C.

What potential difference between the plates will cause the thread to assume an angle of 30.0 deg with the vertical

## Homework Equations

$$Delta(V) = Ed = \frac {F_{elec} * d} {q} = \frac {(mg)*(d)*tan(30)} {q}$$

## The Attempt at a Solution

$$\frac {(2.90*8.90)*(0.05)*tan(30)} {9.70*10^{-6}}$$

The online program complains that its wrong, I'm wondering is the equation correct?

g=9.8 not 8.9?

g=9.8 not 8.9?

That was actually a typo, I used 9.8 and still no luck.

The computation comes out to:

$$-9.38*10^{-7}$$

Can anyone confirm this?

Last edited:
ranger
Gold Member
Convert 2.90 from g to kg. Also you are using 9.70×10^-6 C in the denominator, but the initial value was 9.70×10^6 C.

Convert 2.90 from g to kg. Also you are using 9.70×10^-6 C in the denominator, but the initial value was 9.70×10^6 C.

The mass was what threw it off, actually Q was 10^-6, I guess copying it over from the flash page removed the negative, though I had that in my solution. Also I figured out the answer. THanks!

Last edited:
http://www.krellinst.org/UCES/archive/resources/trig/node10.html" [Broken]

To convert from degrees to radians, multiply degrees by pi/180.

To convert from radians to degrees, multiply by 180/pi.

Last edited by a moderator: