Finding electric field intensity of two spheres

[an_mui]

Any help on this question is appreciated.
Two small spheres each of mass m are suspended by light strings of light L. A uniform electric field is applied in the x direction. If the spheres have equal and opposite charges of magnitude Q, determine the electric field intensity that enables the spheres to be in equillibrium at angle theta. Express your answers in terms of m, L, Q, theta, g and k.
------------ this is the diagram .
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O O ****edit: for some reason the diagram is not
(-) (+) aligned properly when i submit the post
from the diagram I came up with two equations.
Felec + Tcos theta - Fexternal = 0
Tsing theta - mg = 0
Felec = kQ1Q2 / r^2
i don't know what L is for since i don't have it in my equations.

 

[Dr.Brain]

Are you sure the charges are equal and opposite?? ..In that case the two spheres would attract each other , instead of being at equilibrium. I think the two charges are same , Q each and would repulse each other, with Coulomb's force .

The 'L' given in the question is useful sice you can express the distance 'r' between the spheres in equilibrium state in terms of 'theta' and 'L' , to find out 'theta' finally!

BJ

 

[an_mui]

yes i am sure the two charges are equal and opposite.

 

[mukundpa]

do you know r?

then calculate r using L and Theeta

 

[an_mui]

We are to express the answer in terms of m, L, Q , theta, g and k, so we aren't given any numbers. However, my teacher said the two unknowns in this equation are Tension and the electric field intensity

 

[mukundpa]

r = 2*L*cos(theeta)

Fexternal = QE

solve eliminating quantities not required.

 

[an_mui]

is E equal to ...

E = (kQ1Q2) / (Q2L cos (theta))^2 + mgcos (theta) / Qsin (theta)?

 

[mukundpa]

Q1 =Q2 =Q
so

E = kQ/ [(2L cos (theta))^2] + [mgcos (theta) / Qsin (theta)]

 

[mukundpa]

Q1 = Q2 = Q
hence

E = [(kQ) / (2L cos (theta))^2] + [mgcos (theta) / Qsin (theta)]