A spherical shell has uniform charge density 8.8 × 10⁻¹¹ C/m². If a pin hole is made in the surface of the shell then find the electric field in the hole in N C⁻¹. (Take ε₀ = 8.8 × 10⁻¹² S.I. units)
Physics · Electrostatic · Electric field intensity
JEE Mains

Question

A spherical shell has uniform charge density 8.8 × 10⁻¹¹ C/m². If a pin hole is made in the surface of the shell then find the electric field in the hole in N C⁻¹. (Take ε₀ = 8.8 × 10⁻¹² S.I. units)

Physics · Electrostatic · Electric field intensity

G1 Physics · Accepted Answer

Step 1: Convert the density to charge using dq = ρ dV, dq = λ dl, or dq = σ dA as appropriate. Step 2: Integrate over the stated region and then use Coulomb's law/Gauss's law for the field or flux. Step 3: Apply the given radius/position limits and simplify. Final: 5.