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## Homework Statement

Charged metal sphere hanging on an isolated thread of negligible mass is put in a homogeneous horizontal electric field so that the thread makes a 45 degree angle with the el. field. What angle does the thread with the sphere close with the el. field after we remove 40% of the charge from the sphere?

## Homework Equations

1. ##F_g=mg##

2. ##F_g=T \cdot \sin(45)##

3. ##F_{el}=T \cdot \cos (45)##

I have provided image of force diagram.

## The Attempt at a Solution

I can substitute ##F_g## from equation 1 into equation 2 and get:

##mg=T \cdot \sin(45)##

Then I find expression for T in equation 3:

##T=\frac{F_{el}}{\cos (45)}##

and substitute it into second equation:

##mg=\frac{F_{el}}{\cos (45)} \cdot \sin(45)##

##mg=F_{el} \cdot \tan(45)##

I can express electric force as a product of electric field and charge of sphere:

##mg=q \cdot E \cdot \tan(45)##

I haven't gotten further than this. How do I show what happens with an angle when the charge is reduced 40%?