A static, spherically symmetric cloud of charge sits in vacuum with its centre at the…

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 static, spherically symmetric cloud of charge sits in vacuum with its centre at the point

O

. A probe measures the magnitude

E

of the electric field at several distances

r

from

O

; the field is found to point radially outwards everywhere. The readings are Data (distance

r

, field magnitude

E

r=1.0\,\mathrm{cm}

E=5.75\times10^{3}\,\mathrm{V\,m^{-1}}

;

r=2.0\,\mathrm{cm}

E=11.5\times10^{3}\,\mathrm{V\,m^{-1}}

;

r=4.0\,\mathrm{cm}

E=23.0\times10^{3}\,\mathrm{V\,m^{-1}}

;

r=6.0\,\mathrm{cm}

E=20.0\times10^{3}\,\mathrm{V\,m^{-1}}

;

r=10.0\,\mathrm{cm}

E=7.19\times10^{3}\,\mathrm{V\,m^{-1}}

. Translate these readings into a charge distribution. In your working name the Gaussian surface you use and the symmetry that justifies it. ((a)) Show that the readings fit a ball of uniform volume charge density, the simplest distribution consistent with them, and find its radius

R

. ((b)) Find the total charge

Q

of the ball. ((c)) Find the uniform volume charge density

\rho

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