Two metal spheres, one of radius R and the other of radius $$2R$$ respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

Question

Two metal spheres, one of radius R and the other of radius $$2R$$ respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

Infinity Learn · Accepted Answer

when spheres are kept in contact, charge redistribution takes place to get same potential. Total combined charge $$=$$ $$20$$$$π$$$$R2$$σ. Potential of both the spheres become equal, hence Q $$=$$ $$QI2$$ where Q is the charge on sphere of radius R and QI is the charge on sphere of radius $$2R$$.Thus charge on sphere of radius R becomes $$20$$$$π$$$$R2$$σ$$3$$ , while charge on sphere of radius $$2R$$ becomes $$40$$$$π$$$$R2$$σ$$3Hence$$ new charge densities will beσ$$1=53$$σ, σ$$2=56$$σ

	Column-I		Column-II
i.	Electric field for r < R₁	p.	is constant for q₂ and vary for q₁
ii.	Electric potential for r < R₁	q.	is zero for q₂and vary for q₁
iii.	Electric potential for R₁ < r <R₂	r.	is constant
iv.	Electric field for R₁ < r <R₂	s.	is zero

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density $σ$ . They are brought in contact and separated. What will be the new surface charge densities on them?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density $σ$ . They are brought in contact and separated. What will be the new surface charge densities on them?