Coulomb's Law and Electrical Fields

[Yut]

Homework Statement

The tine sphere at the end of the weightless thread has a mass of .60g. It is immersed in air and exposed to a horizontal electric field of strength 700 N/C. The ball is in equlibrium in the position shown. What are the magnitude adn sign of the charge on the ball?

Homework Equations

F=qE
Gravitationa Force= mg
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/10994667_10152670641336806_932307476_n.jpg?oh=9257cdd3e8de5465969a5ec980ec995b&oe=54EDB2B7&__gda__=1424855811_d63d4b9c3de86b44377f76cc1112f998

The Attempt at a Solution

So, since the ball in the equlibrium the forces are balanced.
force downwords due to gravity
mgcosθ
Since the ball moves towords the E field, it should have a negative charge.

So
Fx: F(electrical field)- mgsin =0
qE= mgsinθ
q= mgsinθ / E

I don't get the right answer,
the answer should be -3.1qC

 

[AdityaDev]

F and mg are perpendicular. So mg can't balance the force. Hint: you have forgot to consider another force.

 

[Yut]

Is it the force due to the other charge, which will be + and equalt to kq^2 / r^2... and I would find R using sinθSorry, I mized it with other problem.
What other force there could be?

 

[AdityaDev]

Its the force exerted by the string. What would have happened if the string was absent? The ball would have moved away. But the string stops and holds the ball inplace. So consider tension force. Draw free body diagram. You should get $T_y=mg$ and $T_x=F_E$

 

[Yut]

Oh, I completely forgot about that, and then it will be Tcosθ, and you find T using the mg=Tsinθ
the euqation there fore will be
F(electrical)- Tsinθ-mgcosθ= 0
and you solve for F(electrical)
F(electrical) = qE

and then you look for q

 

[AdityaDev]

Again... I told you F has nothing to do with mg. Its just $F=Tsin\theta$ and $mg=Tcos\theta$. Find T from 2nd equation and put it on first equation.

 

[Yut]

Yes! Here the set up that gave me the right answerhttps://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/11014718_10152670767961806_1607350090_n.jpg?oh=c796df67fefef907f1ccfe3fbafe9f57&oe=54ECB140&__gda__=1424800785_7febf55bcb55aca57d3a84e1bb4b6827