Question

Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of a given charge configuration? (c) [4 marks] Find the electric field vector for all points outside the charged sphere. (d) [2 marks] Derive Gauss's law in differential form from its integral form.

Answer 1

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