A solid insulating sphere of radius a = 5.9 cm is fixed at the origin of a co-or

Question

A solid insulating sphere of radius a = 5.9 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density =-409 pC/m. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b 12.3 cm, and outer radius c = 14.3 cm 1) What is Ex(P), the x-component of the electric field at point P, located a distance d 39 cm from the origin along the x-axis as shown? 2409.8 N/C Submit 2) What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity 2035.9 Submit 3) What is V(a), the electric potential at the outer surface of the insulating sphere? Define the potential to be zero at infinity -7243.5 Submit 4) What is V(c) - V(a), the potentital differnece between the outer surface of the conductor and the outer surface of the insulator? Submit 5) A charge Q = 0.0637uc is now added to the conducting shell. what is V(a), the electric potential at the outer surface of the insulating sphere, now? Define the potential to be zero at infinity Submit

Explanation / Answer

total charge of the inner sphere,

Q = rho*Volume of the sphere

= -409*10^-6*(4/3)*pi*0.059^3

= -3.52*10^-7 C

1) at point P,

Ex(P) = k*Q/r^2

= 9*10^9*(-3.52*10^-7)/0.39^2

= -2.08*10^4 N/c

2) V(b) = k*Q/b

= 9*10^9*(-3.52*10^-7)/0.123

= -2.57*10^4 V

3) V(a) = k*Q/a

= 9*10^9*(-3.52*10^-7)/0.059

= -5.37*10^4 V

4) V(c) - V(a) = V(b) - V(a)

= -2.57*10^4 - (-5.37*10^4)

= 2.80*10^4 V

5) V(a) = k*Q/a + k*Q'/c

= -5.37*10^4 + 9*10^9*0.0637*10^-6/0.143

= -4.97*10^4 V

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