Can someone please help that actually knows how to work this problem. I already

Question

Can someone please help that actually knows how to work this problem. I already submitted it once and the person who answered was wrong on both. Thank you in advance. This problem is killing me! Please show all work. I keep doing something wrong. Thank you! :)

Question: Two spheres with uniform surface charge density, o...

Two spheres with uniform surface charge density, one with a radius of 7.4 cm and the other with a radius of 4.3 cm, are separated by a center-to-center distance of 38 cm. The spheres have a combined charge of +55C and repel one another with a force of 0.66 N. Assume that the charge of the first sphere is greater than the charge of the second sphere.

Part A

What is the surface charge density on the sphere of radius 7.4?

Express your answer using two significant figures.

1=  C/m2  

Part B

What is the surface charge density on the second sphere?

Express your answer using two significant figures.

Explanation / Answer

Charge on sphere 1= q1

Charge on sphere 2= q2

Distance between spheres = r = 0.38m

Radius of sphere 1= r1=0.074m

Radius of sphere 2= r2=0.043m

Surface area of sphere 1=A1= 4r12 = 4*3.14*0.074^2 = 0.0688 m^2

Surface area of sphere 2= A2 = 4r22 = 4*3.14*0.043^2 = 0.023 m^2

Combined charge = q1+q2= 55µC

Thus q2= 55µC - q2 ------------(1)

Force on sphere 1 by sphere 2= F= kq1q2/r^2

Plugging values,

0.66=(9*10^9**q2*(55*10^-6-q2))/(0.38^2)

Gives, q2= 1.93*10^-7 C

From (1), q1= 55*10^-6 – q2 = 55*10^-6 - 1.93*10^-7 = 5.5*10^-5 C

A)

Surface charge density of sphere 1= total charge/ surface area = 1=q1/A1= (5.5*10^-5)/( 0.0688) = 0.8*10^-3 C/m^2 = 0.8 mC/m^2

B)

Surface charge density of sphere 2= total charge/ surface area = 2=q2/A2=(1.93*10^-7)/ (0.023) = 8.4*10^-6 C/m^2 = 8.4µC/m^2

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