Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m fr

Question

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

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Nho 5 years 2021-07-19T00:49:11+00:00 1 Answers 402 views 1

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  1. minhkhang
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    2021-07-19T00:50:53+00:00
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    Answer:

    The point that would have the same electric field as P is  z = 0.108 \ m from the center of the sphere.

    Explanation:

    From the question we are told that

      The  radius of the sphere is  r = 0.30 \ m

       The Electric field at point P is  E = 15000N/C  

        The distance of point P from the center is D = 0.50 \ m

    Since the electric is directed radially outward it mean this it would be felt both inside and outside the sphere

    The Electric field inside the sphere at a distance z is mathematically represented as

                E_i = \frac{k q x}{r^3}

    where k is the coulomb’s constant with a  value 9 *10^9 \ kg \cdot m^3 \cdot s^{-4 } \cdort A^{-2 }

                q is the charge

                 

    The Electric field inside the sphere at a distance D  is mathematically represented as            

                    E _o = \frac{k q}{D^2}

    To obtain the point of equal electric field

               E_i = E_o

              \frac{k q z}{r^3} = \frac{kq }{D^2}

     We have that

                 z = \frac{r^3 }{D^2}

    Substituting values

                    z = \frac{(0.3)^3 }{(0.5)^2}

                    z = 0.108 \ m

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