Posted by Physics Lover on Thursday, June 13, 2013 at 4:45am.
Two fixed, nonconductive, isolated rings of radii 25 cm are electrified and brought close to each other so that they are parallel. The distance between them is 1 m. You know that one of them has a charge of 1 nC(Nano Coulomb) evenly distributed on it, but you are not sure about the other. In order to find out what's the charge on the other, you take a charged ball and move it across the axis of the rings until you find its equilibrium position. You measure where that is and get that the equilibrium position is 25 cm from the ring with the known charge. What's the charge in nC of the second ring?
Details and assumptions:
The second ring also has evenly distributed positive charge on it.

Physics  Physics Lover, Thursday, June 13, 2013 at 4:53am
I solved it like this
let charge of the ball be Q
let charge of unkown ring be Q2
let the place where there is equilbrium be
P. This point P is 0.25m from the ring with known charge and and hence 0.75m from the ring with unknown charge.
Now applying coulomb's law at this point P from both the rings and this force must be equal as the point is in chrge equilibrim.
So at point p
(k*Q2*Q)/(0.75)^2 = (k*1*10^9*Q)/(0.25)^2
[As known charge is 1nC)
Solving we get Q2 = 9 nC.
But the answer is incorrect so what should be the correct answer ?
PLEASE HELP !

Physics  Elena, Thursday, June 13, 2013 at 6:58am
Electric field on the axis of the ring at the distance ‘x’ from the center of it is
E = k xq/{sqrt(R²+x²)}³
k=1/4πε₀
The test charge is in equilibrium =>
E₁=E₂
k x₁q₁/{sqrt(R²+x₁²)}³=
=k x₂q₂/{sqrt(R²+x₂²)}³,
q= x₁q₁{sqrt(R²+x₂²)}³/{sqrt(R²+x₁²)}³=
=0.25•1•10⁻⁹•{sqrt(0.25²+0.75²)}³/{sqrt(0.25²+0.25²)}³=
=2.8•10⁻⁹ C = 2.9 nC

Physics  Physics Lover, Thursday, June 13, 2013 at 10:10am
Hey elena but why is my method wrong ?

Physics  idk, Thursday, June 13, 2013 at 2:34pm
wait 2.8 and 2.9 are both wrong.

Physics  finnt, Friday, June 14, 2013 at 2:29am
Physics Lover : The Coulomb formula is only valid for a point, not a ring

Physics  Physics Lover, Friday, June 14, 2013 at 3:23am
Yeah the answer is wrong so what should be correct ?

Physics  Anonymous, Friday, June 14, 2013 at 4:22am
3.73 is the perfect answer. Elena has done it right, but has made some mistake in calculation
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