An isolated, solid conducting sphere of radius is to be charged so that the magnitude…

PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

An isolated, solid conducting sphere of radius

0.15\,\text{m}

is to be charged so that the magnitude of the electric field at a point

0.25\,\text{m}

from its center is

1.50\times10^3\,\text{N/C}

. (a) Determine the magnitude of the total charge that must be placed on the sphere to achieve the specified field magnitude at

0.25\,\text{m}

. (b) Using your answer to part (a), calculate the uniform surface charge density

\sigma

on the sphere after it has been charged. (c) Will the magnitude of the electric field just outside the surface (at

r = 0.15\,\text{m}

) be greater than, less than, or equal to

1.50\times10^3\,\text{N/C}

? Justify your answer.