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Question

A spherical cavity of radius R is cut from a non-conducting sphere of volulme charge density ρ C/m3 as shown in figure. Find the magnitude of the net electric field at point P.


A
ρl3εo
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B
3ρlεo
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C
ρR2εo
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D
ρ(r1+r2)3εo
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Solution

The correct option is A ρl3εo
The above problem can be solved by the superposition of electric fields due to the complete sphere and the cavity (considered to be of charge density ρ C/m3).

Let the electric field at point P due to the whole sphere of radius 4R is E1 as shown in figure.



From figure,
E1=ρr13εo

Similarly electric field at point P due to cavity of unform charge density ρ C/m3 is,
E2=ρr23εo

Now, from superposition principle net electric field at point P will be,
Enet=E1+E2

Enet=ρ(r1r2)3εo

From triangle law,
l+r2=r1

Substituting it in the above equation, we get
Enet=ρ(l)3εo

Thus, magnitude of the net electric field at point P, will be
|Enet|=ρl3εo

Hence option (a) is the correct answer.
Why this question?
Note: Inside a non-conducting cavity electric field is always zero.

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