Electrostatics Problem Solved: Wall Charge and Hanging Ball | Homework Help

[snipez90]

[SOLVED] Electrostats Problem

Homework Statement

Electrostats

http://img266.imageshack.us/img266/7097/phsyfrpic1vu6.png
A wall has a negative charge distribution producing a uniform horizontal electric field. A small plastic ball of mass 0.01 kg, carrying a charge of -80.0 uC, is suspended by an uncharged, nonconducting thread 0.30 m long. The thread is attached to the wall and the ball hangs in equilibrium in the electric and gravitational fields. The electric force on the ball has a magnitude of 0.032 N.

a. On the diagram below, draw and label all the forces acting on the ball:
(picture of x and y-axis with ball at center)

b. Calculate the magnitude of the electric field at the ball's location due to the charged wall and indicate its direction relative to the coordinate axes.

c. Determine the perpendicular distance from the wall to the center of the ball

d. The string is now cut
i. calculate the magnitude and direction of the acceleration of the ball relative to the coordinate axes
ii. describe the resulting path of the ball

Homework Equations

1. E = F/q (electric field)
2. F = ma
3. E = V/d (electric field)

The Attempt at a Solution

a. Ft (tension) drawn in the second quadrant at an angle similar to the angle the string makes with the wall pointed away from ball, mg along the -y axis pointed away from ball, and Fe (electric) along the +x axis pointed away from ball

b. E = F/q = (.032N)/(80x10^-6C) = 400 N/C, pointing left horizontally towards the wall

c. not sure about this one, I have E = V/d => d = V/E, except I don't know where to begin to find the potential difference, perhaps an easier way...

d. i. Fnet = sqrt[(.032N)^2 + (.98N)^2] = .98 N = ma = (.01kg)a => a = 98 m/s^2, directed in 4th quadrant along Ft (tension)

ii. um southeast and away from the ball?

 

[Doc Al]

c. not sure about this one, I have E = V/d => d = V/E, except I don't know where to begin to find the potential difference, perhaps an easier way...

You need to figure out the angle the string makes. To do that, set up the equations for static equilibrium.

d. i. Fnet = sqrt[(.032N)^2 + (.98N)^2] = .98 N = ma = (.01kg)a => a = 98 m/s^2, directed in 4th quadrant along Ft (tension)

Careful. The mass is 0.01 kg. What is mg?

 

[snipez90]

Wow, I totally ignored the equilibrium condition. So just thinking it through theoretically, the angle should be given by arctan(Fe/mg) right? And mg should be .098 .

 

[Doc Al]

So just thinking it through theoretically, the angle should be given by arctan(Fe/mg) right?

Right.