A negative point charge of magnitude Q a 1.7 nc is at the center of a spherical

Question

A negative point charge of magnitude Q a 1.7 nc is at the center of a spherical conducting shell of inner radius a 2.7 cm and outer radius b 3.5 cm. In addition, the conducting sphere carries a net charge of unknown magnitude and sign, Q. (a) The electric field at al points within the material of the conductor (that is, between radius a and radius b) is known to be exactly zero. Use Gauss's Law for a sphere of radius r a e (where e is an infinitesimally small parameter) to determine the surface charge density on the inner cavity wall (that is, the charge density at radius a) (b) What is the magnitude of the electric field just inside the inner wall of the cavity (that is, at radius r a-e, where ris an infinitesimally small parameter)? location is found to be 5.7 kNyc, directed inward toward the conductor what is the surface charge density on the outer surface of the conducting sphere? (d) By considering your answers to parts (a) and (co determine the net (overall charge, Qs on the holow conductor.

Explanation / Answer

a) net charge on inner surface = -(-1.7) nC = 1.7 nC

charge density on inner surface = (1.7 nC)/(4 x 3.14 x 0.0272) = 185.57 nC/m2

b) electric field just inside inner surface = 9 x 109 x 1.7 x 10-9/(0.027)2 = 20.98765432 kN/C

c) electric field just outside shell = kQouter surface/b2

      -5700 = 9 x 109 x Qouter surface/(0.035)2

Qouter surface = -0.775833 nC

charge density = -0.775833 nC/(4 x 3.14 x 0.0352) = -50.4246 nC/m2

d) Qs = 1.7 - 0.775833 nC = 0.92417 nC

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