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Question : Find the electric field at the centre of a ball of radius R with volume charge density rho = a.r, where a is a constant vector and r is a radius vector drawn from ball's centre.
Relevant Equations and attempt at solution : I used the basic formula for electric field due to continuous volume charge density and arrived at an equation which I tried to solve two different ways as shown in image. I am getting different solutions by trying different methods which is not possible.
I have tried to think of a reason for this and my reasoning for this anomaly has been shown in the image.
Please help me in figuring out where my approach went wrong.
Relevant Equations and attempt at solution : I used the basic formula for electric field due to continuous volume charge density and arrived at an equation which I tried to solve two different ways as shown in image. I am getting different solutions by trying different methods which is not possible.
I have tried to think of a reason for this and my reasoning for this anomaly has been shown in the image.
Please help me in figuring out where my approach went wrong.
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