# Method of Image grounded conducting sphere.

1. Dec 23, 2013

### sudipmaity

1. The problem statement, all variables and given/known data

A point charge of 10 coulombs is placed at a distance d= 20cm from the centre of an earthed conducting sphere of radius a= 5cm.Find ① The maximum surface density of charge induced on the sphere. ② The force of attraction on the point charge ③ The Sphere is now Insulated. Calculate the positive charge which must be given to the sphere inorder that the force on the point charge reduces to zero. (ANS. 176. 8C/m2, 5.64X 1012N, 1.906µC.)

2. Relevant equations

1. σmax=q/4πa (d+a) /(d-a)2
2. F=q 2ad /4πε0(d2-a2)2 ~ q2a /4πε0d3; a <<d.
3. (Q+qa/d)/d2 = (qa/d)/(d- a2/d)2 Q= (qa3/d) (2d2 -a2)/(d 2-a2)2
3. The attempt at a solution
Had no trouble finding 1st two questions. Just substituted the given data into the formula. But the answer to the 3rd question is coming 0.344 Coulomb Instead of 1.906 µC. The formulas were used after referring to 3 books on EM. All had the same formula. So there shouldn't be any mistake there. So is my answer wrong/I am forgetting to approximate Something/iS it a printing mistake.I calculated the 3rd one also approximating a <<d.But answer is nowhere near the given one.

Last edited: Dec 23, 2013