Part B through F Please. I have no idea where to start.metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge −q on the outer spherical shell. Take V to be zero when is infinite.Part B Calculate the potential V(r) for ra<r<rb.Express your answer in terms of the given quantities and appropriate constants.Part C Calculate the potential V(r)for r>rb.Express your answer in terms of the given quantities and appropriate constants.Part D Find the potential of the inner sphere with respect to the outer.Express your answer in terms of the given quantities and appropriate constantsPart E Use the equation Er=−∂V/∂r and the result from part (b) to find the electric field at any point between the spheres (ra<r<rb).Express your answer in terms of the given quantities and appropriate constants.Part F Use the equation Er=−∂V/∂r and the result from part (c) to find the electric field at a point outside the larger sphere at a distance r from the center, where r>rbExpress your answer in terms of the given quantities and appropriate constants.

Question
Asked Sep 21, 2019

Part B through F Please. I have no idea where to start.

metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge
+q on the inner sphere and charge −q on the outer spherical shell. Take
V to be zero when is infinite.


Part B
Calculate the potential V(r) for ra<r<rb.
Express your answer in terms of the given quantities and appropriate constants.

Part C
Calculate the potential V(r)for r>rb.
Express your answer in terms of the given quantities and appropriate constants.


Part D
Find the potential of the inner sphere with respect to the outer.
Express your answer in terms of the given quantities and appropriate constants


Part E
Use the equation Er=−∂V/∂r and the result from part (b) to find the electric field at any point between the spheres (ra<r<rb).
Express your answer in terms of the given quantities and appropriate constants.


Part F
Use the equation Er=−∂V/∂r and the result from part (c) to find the electric field at a point outside the larger sphere at a distance r from the center, where r>rb
Express your answer in terms of the given quantities and appropriate constants.

 

 



 

check_circleExpert Solution
Step 1

Given information:

Charge on the inner sphere = +q

Radius of the inner sphere = ra

Charge on the outer spherical shell = -q

Radius of the outer shell = rb

Step 2

Electric potential at r where, ra < r < rb

The equation of electric potential in terms of electric field is given as:

V(o) V(r) E(r). dr
Now consider a spherical gaussian surface of radius "r" such that ra<r<r, the electric field
at "r" is given by
JE.dA
where q is the total charge enclosed by the gaussian surface,
E is the electric field
A is the surface area
Eo is permittivity of free space
Hence electric field at "r" is:
E(r) =
4περγ2
help_outline

Image Transcriptionclose

V(o) V(r) E(r). dr Now consider a spherical gaussian surface of radius "r" such that ra<r<r, the electric field at "r" is given by JE.dA where q is the total charge enclosed by the gaussian surface, E is the electric field A is the surface area Eo is permittivity of free space Hence electric field at "r" is: E(r) = 4περγ2

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Step 3

Part B:

The electric potential...

E(r). dr
V (co) V(r)
Given V () 0, hence
E(r). dr
dr =
4περ
0 4περr2
That implies:
V (r)
4περ
help_outline

Image Transcriptionclose

E(r). dr V (co) V(r) Given V () 0, hence E(r). dr dr = 4περ 0 4περr2 That implies: V (r) 4περ

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