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www.physics.ucla.edu/~jjmc/ph110a06/Soln5.pdf
1.in a uniform electric field, potential at origin is V, and V/2 at (a,0,0),(0,b,0),(0,0,c).The potential at (a,b,c)
2.A metal sphere of radius r caries a total charge Q, what is the force of repulsion between the two hemispheres.?
Ans,kQ2/8r2
3.A spherical capacitor consists of a spherical shell of radius b.This is concentric with a smaller conducting sphere of radius a.If charge given to the inner sphere is q,what should be the charge given to outer sphere so that PE of system is minimum?
Ans.-q
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3 Answers
23just use Ex= - ΔV/Δx = - (Vx - Vo)/x = constant
Vo = V at origin , Vx = V at x
similarly for y and z
for third, suppose you give Q chargeto outermost shell ,
now the electric field between the shells is independent of Q, so the energy stored in that field is always going to be there and you cant minimize it ,
but the electric field at a pt outside the gr8er shell is due to (Q+q)
so if energy is to be minimized,then we hav to see that energy density is minimum , i.e εE2/2 is minimum , that will be when Q+q = 0