The electric field due to point charge 2q at a distance r is E. Now, charge q is uniformly distributed over a thin spherical shell of radius R, the electric field at a distance r/2 (r R) from the centre of the thin spherical shell is E' = .

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(2) 2E. Given: a point charge 2q produces E=(k(2q))/(r²)=(2kq)/(r²) at distance r. Idea: outside a uniformly charged thin shell the field is the same as if the whole charge sat at the centre. The condition r R puts the field point at r/2 well outside the shell, so the shell acts as a point charge q: E'=(kq)/((r/2)²)=(4kq)/(r²) Comparing the two, (E')/E=(4kq/r²)/(2kq/r²)=2. Halving the charge halves the field, but halving the distance quadruples it, so E'=2E.

The electric field due to point charge 2q at a distance r is E. Now, charge q is uniformly distributed over a thin spherical shell of radius R, the electric field at a distance r/2 (r R) from the centre of the thin spherical shell is E' = ________.

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