Determine the total electric flux through the surface of a sphere of radius R centered at O resulting from this line charge.

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An infinitely long line charge having a uniform charge per unit length λ lies a distance d from point O as shown in the figure below. Determine the total electric flux through the surface of a sphere of radius R centered at resulting from this line charge. Consider both cases, where R < d and R > d. (Use any variable or symbol stated above along with the following as necessary: ε0.)

image
(a) when R < d
ΦE =  

(b) when R > d
ΦE = 

 

asked Feb 10, 2012 in Physics by apush ~Expert~ (552 points)
    

1 Answer

+7 votes
 
Best answer

Part A:

If R ≤ d , the sphere encloses no charge and, ΦE = 0

 

Part B:

If R > d , the length of line falling within the sphere is 2 (R^2 − d^2)^1/2

and so

ΦE =  (R^2 − d^2)^1/2  / ε0

 

Here is the exact solution for both steps:

answered Feb 18, 2012 by awesome ~Expert~ (1,479 points)
selected Feb 18, 2012 by apush



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