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?

Answer 1

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

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

                $z = 0.108 \ m$