A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius

PEEWSRIGWETRYqx 2021-12-16 Answered

A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge destiny of +6.37×106Cm2. A charge of 0.500μC is now introduced at the center of the cavity inside the sphere. 
(a) What is the new carge density on the outside of the sphere? 
(b) Calculate the strength of the electric field just outside the sphere. 
(c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?

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Expert Answer

Ronnie Schechter
Answered 2021-12-17 Author has 27 answers

(a) Calculation:
Solve for the new charge density on the outside of the sphere:
As equation (22.10) mentions, the electric field at the surface of a conductor is given by
E=σϵ0
We use the same technique as an example (22.5), the electric field at the surface of a charged conducting sphere is given by
E=14πϵ0Qr2
Substituting from the previous calculation and solve for the charge density on the outside of the sphere, then we get
σout=Eϵ0
=14πϵ0Qr2ϵ0
=Q4πr2
=0.5×106C4π(0.25m)2
=6.366×107Cm2 Calculation:
In order to evaluate the new charge density on the outside of the sphere, we use the following relation:
σw=σσout
=6.37×106Cm26.366×107Cm2
=5.733×106Cm2
So, the new charge density on the outside of the sphere is 5.733×106Cm2

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Becky Harrison
Answered 2021-12-18 Author has 40 answers
(b) Calculation:
Solve for the strength of the electric field just outside of the sphere:
As equation (22.10) mentions, the electric field at the surface of a conductor is given by
E=σϵ0
=5.733×106Cm28.854×1012C2Nm2
=6.475×105NC
So, the strength of the electric field just outside of the sphere is 6.475×105NC

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Don Sumner
Answered 2021-12-27 Author has 35 answers

(c) Calculation:
As equation (22.8) mentions, the electric flux through a spherical surface inside the inner surface of the sphere is given by
ϕE=Qenclosedϵ0
=0.5×106C8.854×1012C2/Nm2
=5.647×104Nm2/C
So, the electric flux through a spherical surface inside the inner surface of the sphere is 5.647×104Nm2/C

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