Two spherical shells have a common center. A −1.6 × 10−6 C charge is spread uniformly over the inner shell, which has a radius of 0.050 m. A +5.1 × 10−6 C charge is spread uniformly over the outer shell, which has a radius of 0.15 m. Find the magnitude and direction of the electric field at a distance (measured from the common center) of (A) 0.20 m, (B) 0.10 m, and (C) 0.025 m.

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nuuk nuuk · Answer 1 · 2019-07-31T13:09:56+02:00

Answer:Given below

Explanation:

given

charge on inner sphere=-[tex]1.6\times 10^{-6} C[/tex]

Charge on outer sphere =[tex]5.1\times 10{-6} C[/tex]

Consider a gaussian surface of radius (a)0.20 m

net charge inside =[tex]3.5\times 10^{-6} C[/tex]

Electric field[E]=[tex]\frac{KQ}{r^2}[/tex]

E=[tex]\frac{9\times 10^{9}\times 3.5\times 10^{-6}}{0.2^2}[/tex]

E=[tex]787.5\times 10^3 N/C[/tex]

Field direction is outward normal

(b)r=0.1m

Charge enclosed=[tex]-1.6\times 10^{-6}[/tex]

Electric field[E]=[tex]\frac{KQ}{r^2}[/tex]

E=[tex]\frac{9\times 10^{9}\times 1.6\times 10^{-6}}{0.1^2}[/tex]

E=[tex]-1440\times 10^{3} N/C[/tex]

Field direction is Inward normal

(c)r=0.025 m

As the guaussian surface is inside the smaller sphere therefore electric field is zero.