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 spherical insulator of radius R is charged uniformly with a charge Q

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?
Answer» Solution :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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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?

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