One of the hazards facing humans in space is space radiation: high-energy
charged particles emitted by the sun. During a solar flare, the intensity of
this radiation can reach lethal levels. One proposed method of protection for
astronauts on the surface of the moon or Mars is an array of large,
electrically charged spheres placed high above areas where people live and
work. The spheres would produce a strong electric field \(\vec{E}\) to deflect
the charged particles that make up space radiation. The spheres would be
similar in construction to a Mylar balloon, with a thin, electrically
conducting layer on the outside surface on which a net positive or negative
charge would be placed. A typical sphere might be \(5 \mathrm{~m}\) in diameter.
Suppose that to repel electrons in the radiation from a solar flare, each
sphere must produce an electric field \(\vec{E}\) of magnitude \(1 \times 10^{6}
\mathrm{~N} / \mathrm{C}\) at \(25 \mathrm{~m}\) from the center of the sphere.
What net charge on each sphere is needed?
A. \(-0.07 \mathrm{C}\)
B. \(-8 \mathrm{mC}\)
C. \(-80 \mu\) C
D. \(-1 \times 10^{-20} \mathrm{C}\)