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Plzzzzzzzzzzzzzzoooooooooooooooooooolkoolook solve question number 7

Plzzzzzzzzzzzzzzoooooooooooooooooooolkoolook solve question number 7

Question Image
Grade:11

1 Answers

Pooja
127 Points
one year ago

To find Potential due to a non conducting sphere
total 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 - kQR2/2R3
Vr = 3kQR2/2R- kQr2/2R3

        =kQ/2R3 (3R2 - r2)

Ans is (A)

 

 

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