Question

Three spheres of different radii have the same amount of net charge Q uniformly distributed over the volume of spheres (spheres are non-conducting). The sphere

Answer 1

Answer:

E_1 = E_2 > E_3

Explanation:

Given:

- Charged sphere 1 has a radius = R/2

- Charged sphere 2 has a radius = R

- Charged sphere 3 has a radius = 2R

- All charged non conducting spheres have equal Q charge

Find:

- Rank electric field created by each sphere at distance r = R. Greatest to lowest.

Solution:

- The electric field of a non-conducting uniform distributed charge sphere @ r greater than or equal to radius of the sphere is given by:

                                            r >= radius

                                            E = k*Q / r^2

For spheres 1 and 2, the distance r = R is either on surface or outside the sphere. So,

                                             E_1 = k*Q / R^2

                                             E_2 = k*Q / R^2

Hence, both sphere 1 and 2 have equal Electric field at r = R.

- The electric field of a non-conducting uniform distributed charge sphere @ r less than to radius of the sphere is given by:

                                            r < radius

                                            E = k*Q*r / (Radius)^3

For sphere 3, the distance r = R is within the sphere. So,

                                             E_3 = k*Q*R / 8R^3

                                             E_3 = k*Q/ 8R^2

Hence, sphere 3 has less electric field at point r = R.

So the order is:                    E_1 = E_2 > E_3