(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sphere of radius R has volume charge density = B/r for r < R, where B is a constant and = 0 for r > R. (a) Find the total charge on the sphere. (b) Find the expressions for the electric field inside and outside the charge distribution. (c) Sketch the magnitude of the electric field as a function of the distance r from the sphere’s center

2. Relevant equations

3. The attempt at a solution

I got the charge by integrating (4 pi B r dr) over 0 to R as (2 pi B [R^2]). For the part b, that's where I am confused.The solution that I have and the answer that I got are different as the approach is different.

What I have done is:

Q/(Q inside) = (4/3 pi R^3)/(4/3 pi r^3). Substituting Q in this equation from above and using the Gauss' law, I got E = (B r)/(2 R ε0)

But in the solution:

For r<R, they have just simply substituted Qinside = (2 pi B [r^2]) and got E = B/(2 ε0)

For r>R, they have just simply substituted Qinside = (2 pi B [R^2]) and got E = [B(R^2)]/[2 (r^2) ε0]

What here I am confused is 2 things.

1. How does the total charge become the inside charge as the solution says.

2. Notice the Q inside for r<R, it has small r but r>R has big R.

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# Homework Help: Find the charge and electric field.

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