A nonconducting spherical shell problem

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SUMMARY

The discussion focuses on determining the constant A for a nonconducting spherical shell with inner radius a = 2.00 cm and outer radius b = 2.40 cm, which has a charge density p = A/r. The goal is to ensure a uniform electric field within the shell, where a ≤ r ≤ b. The established solution indicates that A must equal 1.79 × 10-11 C/m to achieve this uniformity. The user initially attempted to apply the equation E = kq/r2 but struggled with the variable nature of r within the specified range.

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A nonconducting spherical shell of inner radius a=2.00 cm and outer radius b = 2.40 cm has (withing its thickness) a positive charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q=45.0 fC is located at that center. What value should A have if the electric field in the shell (a[tex]\leq[/tex]r[tex]\leq[/tex]b) is to be uniform?

I know the answer that A value is 1.79[tex]\times[/tex]10-11. The problem is I don't know how to solve it. I don't even know which equation I should use. I tried to start with E = kq/r2, but what is the value of r. It is not specified where should I calculate.

Please help.
Thank you.
 
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r can have any value between a and b. It is a variable, with no specific value.

Do you know what charge the "q" refers to in your equation for E?
 

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