How Do You Calculate Tension and Charge in Electromagnetic Problems?

[MiniOreo1998]

Homework Statement

Charge 1 (0.15 kg) in the following diagram is hanging from a light insulating thread, as shown. Charge 2 is brought close and pulls charge 1, deflecting the string away from the vertical axis. The charges have the same magnitude, but charge 1 is negative.

A) Find the tension in the thread

B) Find the charge on charge 2. Is it positive or negative? Explain your reasoning.

I'm satisfied with my answers, however, I'm almost certain I haven't "listed" everything correctly. (example, putting F_T in the wrong place where a different notation should be listed...)

I'm taking notes from the tips that I've been given in previous threads (just want to make it clear that I'm actually storing this information in order to avoid having to scramble every time a new problem arises).

Homework Equations

[/B]
Fg = m g
Fe= K q₂ / r²

The Attempt at a Solution

[/B]
A)

Ft = m g
Ft = (0.15) (9.8) / cos 40
Ft = 1.9

The tension in the thread is 1.9 N

B)

Ft = k q² / r²
Fe = (9.0 x 10⁹) q² / 0.4²
q = √ (0.40²) (1.9 sin40) / 9.0 x 10⁹
q = 4.7 x 10^-6 C

Charge 1 (given as negative) attracts Charge 2, thus charge 2 is positive.

 

[BvU]

I agree: reading

Ft = m g​

on one line, and then

Ft = (0.15) (9.8) / cos 40​

on the next makes my skin crawl. The 1/cos(40) seems to come out of the blue sky. Something like

Ft_y = m g
| Ft | = (0.15) (9.8) / cos 40​

is more understandable. You can then continue with

Ft_x = | Ft | sin(40) = k q² / r² etc​