1.

A spherical insulator of radius R is charged uniformly with a charge Q throughout its volume and contains a point charge `Q/16` located at its centre. Which of the following graphs best represents qualitatively, the variation of electric field intensity E with distance r from the centre?A. B. C. D.

Answer» Correct Answer - A
For `(x lt R),=(Qx)/((4)/(3)piR^(3)3epsi_(0))+(Q//16)/(4piepsi_(0)x^(2))`
`(dE)/(dx)=0implies(Q)/(4piepsi_(0))=((1)/(R^(3))-(2)/(16x^(3)))=0`
`(d^(2)E)/(dx^(2))=(6Q)/(4piepsi_(0)(16x^(4)))gt0`
`thereforeAt x=(R)/(2),E` is minimum.
For `(x gt R), E=((Q+Q//16))/(4piepsi_(0)x^(2))`


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