Explain why the electric field strength is zero

[MightyMeanie]

I am stuck on my physics homework. I can manage the latter question, how ever when i work out the first one my working out has no rhyme nor reason (nor a right answer). Any help will be great.

A small metal sphere on an insulating rod is placed on a top pan balance, as shown in the diagram below. An identical metal sphere carrying a charge of 2Q on an insulating rod is brought into contact with th sphere on the balance so each sphere acquires the same charge.

When the two spheres are a separation of 68 mm, the top of the pan balance reading increases by 2.1 x 10 ^-3 N. Calculate the charge, Q, on each sphere.

Explain why the electric field strength is zero at the midpoint between the two charge.​

 

[MightyMeanie]

sorry just read the sticky after posting
This is how i attempted to do it, but then realized how completely stupid and random it was
F/Q = E = V/d -> v/o = (2.1 x 10 ^ -3) / 2 -> 1.05 x 10 ^-3

(1.05 x 10 ^ -3) / 0.068 = (2.1 x 10 ^ -3) / Q
Q= (2.1 x 10 ^-3) / (1.544 x 10 ^ -3)
= 0.136 C which is stupid

 

[dduardo]

Coulomb's law states:

F = (k*q1*q2)/r^2

q1 = Q
q2 = 2Q
r = 68mm
k= Boltzmann constant (See your book for this value)
F = 2.1mN

Solve for Q

Once you have Q it should be easy to figure out the electric field due to each charge.

 

[MightyMeanie]

thank you!