Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R.From the expression for E=kQ

Question

Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R.From the expression for E=kQ/r2 for r>R and E=kQr/R3 for r
Only need C & D. It asks for specfic points that I don’t know how to find. I just know the general shape of the graph.

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RuslanHeatt 4 years 2021-07-15T02:51:45+00:00 1 Answers 84 views 0

Answers ( )

  1. phucdien
    0
    2021-07-15T02:53:19+00:00
    Reply

    Answer:

    Vb = k Q / r        r <R

    Vb = k q / R³ (R² – r²)    r >R

    Explanation:

    The electic potential is defined by

                 ΔV = – ∫ E .ds

    We calculate the potential in the line of the electric pipe, therefore the scalar product reduces the algebraic product

                 VB – VA = – ∫ E dr

    Let’s substitute every equation they give us and we find out

    r> R

               Va = – ∫ (k Q / r²) dr

               -Va = – k Q (- 1 / r)

    We evaluate with it Va = 0 for r = infinity

              Vb = k Q / r        r <R

             

    We perform the calculation of the power with the expression of the electric field that they give us

               Vb = – int (kQ / R3 r) dr

      We integrate and evaluate from the starting point r = R to the final point r <R

             Vb = ∫kq / R³ r dr

             Vb = k q / R³ (R² – r²)

    This is the electric field in the whole space, the places of interest are r = 0, r = R and r = infinity

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