Field inside a thin spherical shell of radius R carrying total charge Q. Which statement is correct?

Field inside a thin spherical shell of radius R carrying total charge Q. Which statement is correct?

• A. E_inside = Q / (4π ε0 r^2); E_outside = 0
• B. E_inside = Q / (4π ε0 r^2); E_outside = Q / (4π ε0 r^2)
• C. E_inside = 0; E_outside = Q / (4π ε0 r^2)
• D. E_inside = Q / (4π ε0 R^2); E_outside = Q / (4π ε0 r^2)

Answer: (C)

Field inside a thin spherical shell is zero, while outside the field behaves as if all the charge were at the center. This comes from Gauss’s law and the symmetry of the problem: for any closed surface entirely inside the shell, the enclosed charge is zero, so the net flux is zero and the electric field must vanish everywhere inside. For points outside the shell, the charge Q acts like a point charge at the center, giving a radial field with magnitude E = (1/4π ε0) Q / r^2. So the correct statement is that the field inside is zero, and the field outside is Q/(4π ε0 r^2). The other options either assign a nonzero field inside (which contradicts Gauss’s law for zero enclosed charge) or misstate the outside-field dependence.

Field inside a thin spherical shell is zero, while outside the field behaves as if all the charge were at the center. This comes from Gauss’s law and the symmetry of the problem: for any closed surface entirely inside the shell, the enclosed charge is zero, so the net flux is zero and the electric field must vanish everywhere inside. For points outside the shell, the charge Q acts like a point charge at the center, giving a radial field with magnitude E = (1/4π ε0) Q / r^2.

So the correct statement is that the field inside is zero, and the field outside is Q/(4π ε0 r^2). The other options either assign a nonzero field inside (which contradicts Gauss’s law for zero enclosed charge) or misstate the outside-field dependence.