Two spheres with uniform surface charge density, first with a radius of 7.5cm, a

Question

Two spheres with uniform surface charge density, first with a radius of 7.5cm, and the second with a radius of 4.6 cm, are separated by a center to center distance of 33cm. The spheres have a combined charge of 55*10^-6C and repel one another with a force of.73N Assume q1 >q2. What is the surface charge density of the second sphere?

Any help with this problem would be great. I found the surface charge density for the first , but cannot find the surface charge density for the second sphere. Thanks

Explanation / Answer

for point charges we can use F=k*q1*q2/r^2
(but since size of spheres is not negligible, problem is more complicated)
my guess is that we are expected to treat them as point charges, but express charges in terms of surface density.


q1+q2=55uC

r=0.33m

r^2=0.1089m^2

k=9*10^9

F=0.73N

F=k*q1*q2/r^2

q1*q2=F*r^2/k
q1*(55uC-q1)=0.73*0.1089/9*10^9

-q1^2+55*10^-6*q1-0.000000000008833=0

a=-1
b=0.000055
c=-0.000000000008833
then solve quadratic equation:
q1=[-b+(b^2-4ac)]/(2a)
or
q1=[-b-(b^2-4ac)]/(2a) (but this one will not work since both q1 and q2 must be positive)

then find q2:
q2=55uC-q1

to get surface charge, first find surface A of the sphere

then charge density is

p1=q1/A

p2=q2/A

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.