A solid insulating sphere of radius a 5 cm is fixed at the origin of a co-ordina

Question

A solid insulating sphere of radius a 5 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density p-246 HC/m. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b 12.9 cm, and outer radius c 14.9 cm 1) What is Ex(P), the x-component of the electric field at point P, located a distance d 32 cm from the origin along the x-axis as shown? N/C Submit You currently have 5 submissions for this question. Only 15 submission are allowed You can make 10 more submissions for this question. 2) What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity V Submit You currently have 8 submissions for this question. Only 15 submission are allowed You can make 7 more submissions for this question. Your submiss 4,528 1010 x Computed value: -45280000000 Submitted: Tuesday, September 18 at 12:36 PM Feedback: 3) What is V(a), the electric potential at the outer surface of the insulating sphere? Define the potential to be zero at infinity 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-0.0526uC 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

Explanation / Answer

given solid insulating sphere

a = 5 cm

b = 12.9 cm

c = 14.9 cm

rho = -246 uC/m^3

1) for d > c

From gqauss law

E*4*pi*d^2 = rho*4*pi*a^3/3*epsilon

d = 32 cm

E = 4*pi*k*rho*a^3/3*d^2 = -11295.62092967 V/m ( along -ve x axis)

2) inner surface of the conducting shell

V(b) = k*rho*4*pi*a^3/3*b

V(b) = 4*pi*k*rho*a^3/3b = -8966.446381 V

3) outer surface of the insluating sphere

V(a) = k*rho*4*pi*a^3/3a

V(a) = 4*pi*k*rho*a^2/3 = -23133.4316 v

4) V(c) = 4*pi*k*rho*a^3/3c = -7762.8965 V

Vc - Va = 15370.53506846 V

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