# Balls in a magnetic field

#### theneedtoknow

2 identical small balls hang in a 100, 000 N/C electric field as shown. They have charges of 100 and -100 nC respectively. The string length is 50cm and the angle each makes with the vertical is 10 degrees. Find the mass of the balls.

http://img514.imageshack.us/img514/633/phees.th.jpg [Broken]

2. Relevant equations

F = Eq , F = k|q1||q2|/r^2, F = mg
k = 9 x 10^9 Nm^2/C^2

3. The attempt at a solution

For the left ball :

Fx = Tsina - Eq - kq^2/(sina^2) = 0
T = (Eq + kq^2/sina^2)/ sina

Fy = Tcosa - mg = 0
m = Tcosa / g

m =(cosa/g) * (Eq + kq^2/sina^2) / sina

but when i evaluate this with a = 10 , g = 9.8, E = 100 000, k = 9x10^9, q = 1 x 10^7
i get m = 7.5 grams

the answer in the back of the book is 4.1 grams

where am i going wrong?

Last edited by a moderator:

#### LowlyPion

Homework Helper
First of all, its not a magnetic field. Looks like a uniform E-field of 100,000 V/m.

And it makes a difference.

Left to themselves the + and - charges on the balls would be attractive, not repulsive. Hence the m*g AND the attractive forces between the balls are being balanced by the attraction of the balls toward their respective potentials.

#### theneedtoknow

ohhhhhhhh thats right , thank you!!!

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