Charge in conductors

songoku

1. The problem statement, all variables and given/known data
A sphere conductor of radius 18 cm has potential 27 Volt. Another sphere conductor has potential 18 Volt. Both of them are connected and the combined potential is 24 Volt. Find:
a. the charge of second sphere
b. the charge of each sphere now


2. Relevant equations
Q = CV
V = kQ / r

3. The attempt at a solution
a.
V₁ = k.Q₁ / r₁
27 = 9 x 10⁹ x Q₁ / (18 x 10^-2)
Q₁ = 5.4 x 10^-10 C

Then I don't know how to continue.....

AGNuke

Try using conservation of charge.

EDIT: Are those two sphere of same radius?

ehild

You can calculate also the final charge Q1' on the first sphere, as its potential is known.
As for the second sphere, kQ₂/R₂=18 and kQ'₂/R₂=24. From here, you can find the ratio Q2'/Q2. As AGNuke said, the sum of the charge on the spheres is conserved: Q1+Q2=Q1'+Q2'.

ehild

songoku

I don't know but maybe they are not

V' = k Q1' / r₁
24 = 9 x 10⁹ x Q1' / (18 x 10^-2)
Q1' = 4.8 x 10^-10 C

kQ₂/R₂=18 ; kQ'₂/R₂=24
So Q2'/Q2 = 24/18 = 4/3

Q1+Q2=Q1'+Q2'
5.4 x 10^-10 + Q2 = 4.8 x 10^-10 + 4/3 Q2
Q2 = 1.8 x 10^-10 C

Q2' = 2.4 x 10^-10 C


If the spheres have same radius, then the combined potential should be: (27 + 18)/2 = 45/2 V. Am I correct in this case?

Thanks

ehild

Your solution is excellent and you are right, if the radii were the same the final voltage would be 22.5 V.

ehild

songoku

OK. Thanks a lot