An insulating sphere of radius 15cm that carries a charge of 10 uC is placed at

Question

An insulating sphere of radius 15cm that carries a charge of 10 uC is placed at the center of a hollow charged conducting sphere (inner radius =25cm outer radius = 35 cm). the outer conducting sphere carries a total excess charge of -5uC. By constructing a appropriate gaussian surface in each case, use Gauss's law to determine the magnitude and direction of the electric field at the following radial distances from the common center of spheres: A) r = 10cm B) r = 20cm C) r = 30cm D) r = 45cm E) what is the surface charge density on the outer surface of the conducting sphere? I WILL RATE IF I SEE WORK. THANKS

Explanation / Answer

Charge on insulating sphere = 10 uC Induced charge on inner surface of conductor = -10C Charge on outer surface of conductor = 10 uC Volume of insulating sphere = 4/3 * pi * .15^3 = .0141 m^3 Volume enclosed at 10 cm = .00419 m^3 Charge enclosed at r = .10 = .00419 / .0141 * 10 = 2.96 uC A) E10 = k * .2.96 uC / .10^2 B) E20 = k * 10 uC / .20^2 C) E30 = 0 no field within conductor D) D45 = k * 10 uC / .45^2 total enclosed charge is 10 uC E) density = 10 uC / A where A = 4 * pi * .35^2 area of sphere

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