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Electricity
Electric field inside a cavity of a non conducting uniform sphere is constant.Can anyone pls explain me why is it uniform and if it is uniform what is its value??
Comments (13)
even i thought the same thing before but IIT 2007 had asked a question on the same concpt ..
A spherical portion has been removed from solid sphere having charge uniformly distributed in its volume as shown in the figure.The electric field inside the emptied space is
(A) zero everywhere (B)non zero and uniform (C) non uniform (D) zero only at its centre.
Answer is option B....I checked out many solutions but the answer is B..even i am not understanding why....pls help me someone.....
For this question use superimposibility of forces ...
Let O and O' be the centres of the sphere and of the cavity respectively
Let a be the seperation bw the 2 centres
Lets take a point P inside the conductor at a distance x from O and y from O'
imagine that there was no cavity , then the field on P would be ....(1)
and due to the cavity individually it would be ....(2)
therefore the net electric field due to these two is (1)  (2)
Using addition of vectors we get the above result as
which is a constant and is zero only if the 2 spheres are concentric which is not so in the given question and hence the answer is (b)
PLS VOTE
GOOD THINKING Sachin , I too thought in the same way . Well, there is another interpretation for this problem . Just consider the gaussian surface containing the pt. P as described by Sachin. Calculate the field at that pt. due to the gaussian sphere. Let this be E. Now consider the cavity to contain a negative charge equal( in magnitude) to the charge contained by the portion of the sphere that was removed.Then find the field only due to the removed portion.Let this be E`. Then your required field (due to the remaining portion of the sphere) will be equal to E+E`, which u will find is constant.
This may seem ridiculus but it does serve ur purpose quite well. In case there was no charge in the sphere , but rather u were asked to find the gravitational field at that point then u would have to consider the mass of the cavity as negative. Had it been a conducting sphere then field at any pt. inside the cavity would have been 0.
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