Draw the electric field lines for the system of a point char

Draw the electric field lines for the system of a point charge -2q in the center of two concentric spherical shells carrying uniformly distributed charges +q (total charge) and -q (total charge) as schematically marked in the figure below. Write formulas for the electric field in 3 regions: (1) r

Solution

(1) r < a

Q_enclosed / ₀ = E*(4r²)

=> (-2q) / ₀ = E*(4r²)

=> E = -q / 2₀r²

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(2) a < r < b

Q_enclosed / ₀ = E*(4r²)

=> (-q) / ₀ = E*(4r²)

=> E = -q / 4₀r²

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(3) r > b

Q_enclosed / ₀ = E*(4r²)

=> (-2q) / ₀ = E*(4r²)

=> E = -q / 2₀r²