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#linear variation

2 public questions tagged with this topic.

Why does the electric field inside a charged spherical shell vary linearly with distance from the center when a uniform

**Dielectric polarization** when slab inserted, bound charges appear reducing effective field, capacitance increases by factor K, potential difference for constant charge V = Q/C decreases, for constant voltage charge increases. Dielectric constant K = ε/ε₀ >1, e.g., K≈5 for glass. Electrostatic Potential and Capacitance typically assumes no charge inside a spherical shell, leading to E = 0 . However, if misinterpreted as a charged dielectric sphere (common in advanced contexts but not in the PDF), the field varies as E ∝ r . Since the PDF context implies an empty shell or uniform shell charge, E = 0 . Assuming a misinterpretation, the correct context

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Conductors, Electrostatic Shielding and Dielectrics

Why does the electric field inside a uniformly charged spherical shell vary linearly with distance from the center if a

**Dielectric polarization** when slab inserted, bound charges appear reducing effective field, capacitance increases by factor K, potential difference for constant charge V = Q/C decreases, for constant voltage charge increases. Dielectric constant K = ε/ε₀ >1, e.g., K≈5 for glass. Without the point charge, the field inside a uniformly charged spherical shell is zero (Gauss’s law). With a point charge Q at the center, the field inside the shell is due to the point charge only ( E = (1/4 π ε₀) (Q/r²) ), which varies as (1/r²) , not linearly. The question may imply a misunderstanding; in standard electrostatics (per the PDF), the shell

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Conductors, Electrostatic Shielding and Dielectrics