(a) the charge on the insulating sphere C (b) the net charge on the hollow condu

Question

(a) the charge on the insulating sphere
C

(b) the net charge on the hollow conducting sphere
C

(c) the charge on the inner surface of the hollow conducting sphere
C

(d) the charge on the outer surface of the hollow conducting sphere
C

For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose the electric field at a point 14.0 cm from the center is measured to be 3.70 103 N/C radially inward and the electric field at a point 50.0 cm from the center is of magnitude 199 N/C and points radially outward. From this information, find the following. (Include the sign of the charge in your answer.) the charge on the insulating sphere the net charge on the hollow conducting sphere the charge on the inner surface of the hollow conducting sphere the charge on the outer surface of the hollow conducting sphere

Explanation / Answer

a)

q = ?V = ?(4/3*?r^3)
E = kq/r^2 = k?(4/3?r^3)/r^2 = 4k??r/3 = ?r/(3?_0)

A cavity has no charge, which is the same as having two equal and opposite charges. Find the electric field of such an opposite sphere:
E_opp = -?d/(3?_0)
This is the same as above, just using d to denote the distance from the center of the opposite sphere. Because the sphere is centered at h in the sphere, d = r - h:
E_opp = -?(r - h)/(3?_0)

E_cav = E + E_opp = ?r/(3?_0) - ?(r - h)/(3?_0) = ?h/(3?_0)

b)

Negative charge of magnitude q is induced in the inside surface of the conducting sphere
Outside surface of the conducting sphere is now charged with positive charge q.
The sphere being connected to the earth, positive chages move away to the earth through the wire.
The sphere is now charged with negative q charge.

The field at any point on the surface of the sphere or out side the spehere is given by - 9e9 q/r^2 where r is the distance of the point from the centere of the sphere.
The charges behave as if all the charges were concentrated at the center of the sphere.

c)

Please always remember that there is NO static electric field within the bulk of any metal, otherwise current would flow through the metal till the condition I claimed. Hence, when a charge of -0.580 (the UNIT?) is now introduced into the cavity inside the sphere, there must be a change of +0.580 built up on the inner surface. To keep the total charge on the sphere unchanged, the uniformly distributed charge on the out spherical surface must be Q = +(6.90

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