Consider any charge distribution with a charge densityp(f), let v be a spherical region of radius .. Centered at 0, the average electric field E within v has the formula: 1 | E(F)dv = Ēint + Eext .3 where Ent is the average field due to all internal charges v and Eetis the average field due to all external charges v Prove that Eint 1 4TE0 r3 Eext 1 Sv 4TE0 r13 where Pis the electric dipole moment (cycle O) of the internal charge. and V is the region in space. that includes v and P(F)# 0

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Consider any charge distribution with a charge density e(7), let v be a
spherical region of radius Y.. Centered at 0, the average electric field E
within v has the formula:
1
E:
Iar / E(F)dv = Ent + Eot
%3D
where Ent is the average field due to all internal charges v and Eetis the
average field due to all external charges v Prove that
Eint
1
4T€0 r3
Eext
p(T) du'
Jv
4T€0
p13
where p is the electric dipole moment (cycle O) of the internal charge.
and V is the region in space. that includes v and P(F)# 0
3
Transcribed Image Text:Consider any charge distribution with a charge density e(7), let v be a spherical region of radius Y.. Centered at 0, the average electric field E within v has the formula: 1 E: Iar / E(F)dv = Ent + Eot %3D where Ent is the average field due to all internal charges v and Eetis the average field due to all external charges v Prove that Eint 1 4T€0 r3 Eext p(T) du' Jv 4T€0 p13 where p is the electric dipole moment (cycle O) of the internal charge. and V is the region in space. that includes v and P(F)# 0 3
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