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

Question

Two spheres with uniform surface charge density, first with a radius of 7.5cm and the second with a radius of 5.0cm are separated by a center-to-center distance of 33cm. The spheres have a combined charge of 55microC and repel one another with a force of 0.63N. Assume q1 > q2. What is the surface charge density on the first sphere?  What is the surface charge density on the second sphere? Two spheres with uniform surface charge density, first with a radius of 7.5cm and the second with a radius of 5.0cm are separated by a center-to-center distance of 33cm. The spheres have a combined charge of 55microC and repel one another with a force of 0.63N. Assume q1 > q2. What is the surface charge density on the first sphere?  What is the surface charge density on the second sphere?

Explanation / Answer

given q1+Q2 = 55 uC

q1/q2 = 7.5/5 = 1.5

q1 =1.5 q2

q2 + 1.5 q2 = 55 uC

q2 =55/2.5 = 22 uC

q1 = 1.5*22 = 33 uC

surface charge density of q1 is Q1/area = 33uC/4* 3.14* 0.075^2 =4.67 *10^-4 C/m^2

syrface chage densty of q2 = Q2/area = 22uC/4*3.14* 0.05^2 = 7*10^-4 C/m^2

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