QuestionDetails: A solid metal sphere of radus r 1 has a charge +Q.it is surroun

Question

QuestionDetails: A solid metal sphere of radus r1 has a charge +Q.it is surrounded by a concentric spherical metal shell with innerradius r2 and outer radius r3, that has acharge -Q on its inner surface and +Q on its outer surface. In thediagram, point A is located at a distance r4 from thecenter of the spheres. Points B and C are inside the metal shell,very near the outerand inner surfaces, respectively. Point E isjust inside the surface of the solid sphere. Point D is halfwaybetween C and E. Point F is a distance r1/2 from thecenter. (a) Is each of the following potential differences >0,=0,or<0? Briefly explain why in terms of electric field. VB-VA; VC-VB;VD-VC; VF-VE (b) Calculate the potential at location F, VF.Explain your work.

Explanation / Answer

AT POINT C : electric field due to charged solidsphere at a point 'C' which is at a distance r from the centreof the sphere             V= Q1 / 4.R R = ditsance from the centere topoint C R = ditsance from the centere topoint C   potential due to chargedspherical shellat any pont inside the shell           V' = Q2/4 R' R' = radius of the shell positivecharged shell and for negative charged shell,potential at any point inside the shell           V'' = -Q3/4 R'' R''= rdius of the negative chargedshell and for negative charged shell,potential at any point inside the shell           V'' = -Q3/4 R'' R''= rdius of the negative chargedshell from the abve relation we cansolve for net potential at a point C inside the shell at a point C inside shell netpotential at a point C inside shell netpotential          VC = V + V' +V'' V',V'' are the potentials dueto the charged sphererical shell          VC = V + V' +V'' V',V'' are the potentials dueto the charged sphererical shell         
AT POINT A:
simillarly potential at a point A outside the spherical shell           VA = V +V' +V''               = [Q1/ 4.R1 ] + [Q1 /4.R2 ]+[ Q1 /4.R3 ] V , V' and V'' are the potentialsat point A due to Q1,Q and Q3 AT POINT B:
simillarly potential at a point B can be determined by consideringthe potentials due to the three spheres, potential energy on the surface of acharged spherical shell                V'' = +Q / 4.R,
the net potentialat B can be determined by the alzebric sum of the three potentials. b)V = VB-VA;, the sum may be either '+' or '0' or '-' After determining the sum ofthe potnetials if the sum V<0 ,i.e .,
VB<VA;  negative potential difference indiactes the electric field pointsradially out wards from B->A the charged sphere. for V=0 ,E= 0 and F = 0, for V>0, the potential differenceis positive and the electric field points radially out wardsexerting repulsive force on a positive test charge,the electricfield points radially in wards from A->B thecharged sphere. Electric field pointsalways from higher potential to lower potential. b) V = 0 inside at a location F ,there is no field present inside a conducting solid sphere,    if V is not equal to 0,then E will not be zero and there will be net current flow in thesphere which brings all the negative charges accumlate on thesurface of the sphere and equal equal magnitude of positive chargeat the centre which is not possible,since the positive chargesare immobile .

Hence E = 0, => V = 0 .

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