A thick spherical shell of insulating material has inner radius and outer radius

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential

Electricity, Magnetism and Electromagnetism, Ch Electric flux and Gauss's law

Problem

A thick spherical shell of insulating material has inner radius

a=5.0\,\mathrm{cm}

and outer radius

b=10.0\,\mathrm{cm}

. The material carries a uniform volume charge density

\rho=+2.4\times10^{-6}\,\mathrm{C\,m^{-3}}

; the hollow region

r<a

is empty and there is no other charge anywhere. Let

r

be the distance from the centre. ((a)) State the symmetry argument that fixes the direction of

\mathbf{E}

and the single variable it depends on, and say which Gaussian surface it licenses. ((b)) Derive the magnitude of the field in each of the three regions

r<a

a\le r\le b

and

r>b

, in terms of

\rho

a

b

r

and

\varepsilon_0

. ((c)) Evaluate the field magnitude at

r=3.0\,\mathrm{cm}

r=7.5\,\mathrm{cm}

and

r=20\,\mathrm{cm}

, stating the direction where it is not zero.

Browse the problem library