A point charge on a string in equilibrium with electric field

[saw176]

Hi everyone, I took a look at previous questions similar to this one and it seems like I am doing everything correctly, but I still get the wrong answer. Any advice to where I am going wrong would be greatly appreciated!

Homework Statement

A point charge (m=1.0g) at the end of an insulating string of length 55 cm is in equilibrium in a uniform horizontal electric field of 12,000 N/C (which points to the right, in the direction of the pendulum's "swing"), when the pendulum's position is with the charge 12 cm above the lowest vertical position. Determine the magnitude and sign of the point charge.

Homework Equations

Tcos(theta) = mg
Tsin(theta) = qE

The Attempt at a Solution

First I found the angle theta by subtracting the height, 12 cm, from the length of the pendulum string, 55 cm. So the height is 43 cm, and applying cos(theta) = 43/55 I found the angle to be 38.6 degrees.

Next, I took the above sin and cos equations and put sin over cos to get:
tan (theta) = qE / mg
tan (38.6) = q (12,000) / (0.001)(9.80)

Solving for q, I keep getting 6.5 x 10^-7 C, but the correct answer is 7.8 x 10^-7 C. What am I doing wrong? Thanks for your help!

 

[ehild]

I do not see anything wrong in your work. Your result looks right.
The given answer can be wrong. It happens.

ehild

 

[saw176]

Thanks ehild! I actually saw somewhere online else a student saying they got that same answer and wondering where they went wrong, so you just might be right that the book is incorrect!

 

[ehild]

It happens quite often.

ehild