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Grade 12th passAlgebra

Two metal spheres one of radius r and 2r have same surface charge density. They are brought in contact and separated. What will be the new surface charge densities on them

Profile image of M siddharth goutam
7 Years agoGrade 12th pass
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1 Answer

Profile image of Arun
7 Years ago
 
Let q1, q2 be initial charges on spheres with radius R and 2R respectively.
As charge surface charge density of both the spheres is same 
So sigma1=sigma
=> q1/4pir^2 = q2/4pi(2r)^2
=> 4q1=q2
=>total charge = q1+q2 = 5q1
 
when they are joined by a conducting wire , they will have same potential on their surfaces ,
let charges now on each sphere be Q1 and Q2 respectively
=> kQ1/R = kQ2/2R
=> 2Q1=Q2
total charge = Q1+ Q2 = 3Q2
 
as total charge of the system remains conserved
=> 5q1=3Q2 = 3(2Q1) =6Q1
=> Q1 = 5q1/6
 
hence final charge density = kQ1/R = 5kq1/6R

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