E Field of Sphere: Find Magnitude at Distance .05m

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To find the electric field magnitude at a distance of 0.05m from the center of a nonconducting solid sphere with a radius of 0.1m and a uniform volume charge density of 2*10^-6 C/m^3, the correct approach involves using the formula for the electric field inside the sphere. The total charge (Q) was calculated as approximately 8.38e-9 C. The electric field formula for points inside the sphere is E(r) = (1/(4πε₀))(Q/R³) * r. The initial calculation yielded an incorrect value of 30,000 N/C, but the correct electric field at 0.05m is 470 N/C, confirming the necessity of using the appropriate formula for points within the sphere. Understanding the distinction between electric fields inside and outside the sphere is crucial for accurate calculations.
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Homework Statement



A nonconducting solid sphere of radius (R) .1m has uniform volume charge density (2*10^-6 C/m^3 was calculated and verified accurate). Find the magnitude of the e field at a distance (r) .05m from the sphere's center.

Homework Equations

The Attempt at a Solution


flux=E*4*pi*r^2 = Q/Eo
I calculated Q by multiplying the volume charge density by its volume (4/3)*pi*(.1^3) which got me 8.38e-9 C.

I solved for E=Q/(Eo * 4 * pi * r^2) which got me 30000 N/C. But that answer was 470 N/C. What did i do wrong?
 
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you have to use the electric field inside the sphere since r=0.05 m is less than the radius
R= 0.1 m. Electric field inside the sphere at a distance r from the center is

E(r)=\frac{1}{4\pi \epsilon_o}\;\frac{Q}{R^3}\;\; r

where Q is the total charge

reference:http://www.phys.uri.edu/~gerhard/PHY204/tsl56.pdf
 
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