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To find Potential due to a non conducting spheretotal charge inside it be ‘Q’volumetric charge density be ‘ρ’.Let R be the radius of the sphere.We need to calculate potential due to a conducting shell at distance r such that it is inside sphere
We know the relation between volumetric charge density (ρ) and total charge within the volume (Q) :
Q = 4πR33 ρ.......(1)
We also know,
dV = - ∫Edr
We also know the relation between electric field (E) and potential (dV)Let the distance r from centre enclose a small sphere with radius r and charge q.
dE=kq/r2
Q/R3 = q/r3 (from eq 1)
dE = kQr/R3
dV = -∫kQr. dr/R3
= - lim[kQr2/2R3]
Integrating above equation and applying limits from r to R
VR - Vr = -kQR2/2R3 + kQr2/2R3
Now VR = kQR2/R3
kQR2/R3 - Vr = kQr2/2R3 - kQR2/2R3Vr = 3kQR2/2R3 - kQr2/2R3
=kQ/2R3 (3R2 - r2)
Ans is (A)
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