A solid insulating sphere of radius a = 3 cm is fixed at the origin of a co-ordinate system as shown. The sphere is unif

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A solid insulating sphere of radius a = 3 cm is fixed at theorigin of a co-ordinate system as shown. The sphere is uniformlycharged with a charge density ρ = -377 μC/m3. Concentricwith the sphere is an uncharged spherical conducting shell of innerradius b = 12.9 cm, and outer radius c = 14.9 cm.
1. What is V(c) - V(a), the potentital differnece betweenthe outer surface of the conductor and the outer surface of theinsulator?
2. A charge Q = 0.0733μC is now added to the conductingshell. What is V(a), the electric potential at the outer surface ofthe insulating sphere, now? Define the potential to be zero atinfinity.
An infinitely long solid insulating cylinder of radius a = 4.3cm is positioned with its symmetry axis along the z-axis as shown.The cylinder is uniformly charged with a charge density ρ = 29μC/m3. Concentric with the cylinder is a cylindricalconducting shell of inner radius b = 10.1 cm, and outer radius c =12.1 cm. The conducting shell has a linear charge density λ =-0.34μC/m.
3) The charge density of the insulating cylinder is nowchanged to a new value, ρ’ and it is found that the electric fieldat point P is now zero. What is the value of ρ’?
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