The Electric Field of a Charged Spherical Shell Problem: A spherical conducting

Question

The Electric Field of a Charged Spherical Shell

Problem: A spherical conducting shell of inner radius a and outer radius b carries a total charge +Q distributed on the surface of a conducting shell (Fig. a). The quantity Q is taken to be positive.

Suppose the charge at the center is now increased to +6Q, while the charge at the surface of the conductor is changed to -10Q.

(a) Find the electric field interior to the sphere in the region r < a

E = ________ x Q/40r2

(b) Find the electric field interior to the sphere in the region r > b.

E = ________ x Q/40r2

(c) Find the electric field within the conducting shell itself, in the region a < r < b.

E = ________ x Q/40r2

Much love if you can get this. Thanks. ~Lelani <3

Explanation / Answer

(a) the elecctric field at r< a E = k*q_enlosed / r^2 k = (1/4_0) here q_ enclosed     = 6Q (b) the electric field in the region r > b E = k*q_enclosed / r^2 here q _enclosed   = (charge on the conducting shell) - ( charge due to point charge )                                = (- 9Q) + ( 6Q) = - 3Q (c) the elecrtic field in the region a < r < b E = 0 since the charge inside the conductor is zero

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