surface charged density?

Question

Two spheres with uniform surface charge density, first with a radius of 7.5 cm and the second with a radius of 4.7 cm, are separated by a center-to-center distance of 33 cm. The spheres have a combined charge of + 55 uC and repel one another with a force of 0.73 N. Assume q_1>q_2

What is the surface charge density on the second sphere? 

I already got the answer for the first sphere which is 7.8*10^-4 but I can't get the second one. I thought it was 4*10^-6 but its not. please help!! show work and answer please!!

anil bakshi · Accepted Answer

F = 9*10^9 q1 q2/0.33*0.33 = 0.73
q1 q2 = 8.883*10^-12 -------------------- (1)
q1 + q2 = 55 * 10^-6 ---------------------- (2)
=======================
(q1-q2)^2 = (q1+q2)^2 - 4 q1 q2
(q1-q2)^2 = 2989.47*10^-12
(q1-q2) = 54.68*10^-6 ------------------------ (3)
========================================= adding (2), (3)
q1 = 54.84*10^-6 C
q2 = 0.16*10^-6 C
-----------------------------------------------------
surface charge density (1) = q1/4pi r1^2 = 54.84*10^-6 * 14.15 = 7.76*10^-4 C/m^2
surface charge density (2) = q2/4pi r2^2 = 0.16*10^-6 * 36 = 5.76*10^-6 C/m^2

? · Answer

once you connect the two spheres ( which by capacity of ways might desire to be floating an prolonged way away fom the rest to boot) then you particularly are permitting present day to flow between the two to equalise the flair potential. the flair on a around capacitor is proportional to entire can charge / diameter so present day will flow til the two capacitors are on a similar ability while the massive sphere has two times the completed can charge that the small sphere holds. however the massive sphere additionally has two times the outdoors section so the can charge density is an identical.

surface charged density?

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