A total charge Q is distributed uniformly throughout a spherical volume that is centered at 01 and has a radius R. Without disturbing the charge remaining, charge is removed from the spherical volume that is centered at O2, as shown in the figure. Show that the electric field everywhere in the empty region is given by where i is the displacement vector directed from 01 to O2. 4πεο R3' (Hint: Model the sphere as a positively charged sphere with no cavity + negatively charged sphere with negative charge at the location of the cavity. Then pick a point inside the negatively charged sphere (not at its center, since you need to prove the expression is correct for anywhere inside the cavity) and use gauss's law to find the electric field due to each sphere). R
A total charge Q is distributed uniformly throughout a spherical volume that is centered at 01 and has a radius R. Without disturbing the charge remaining, charge is removed from the spherical volume that is centered at O2, as shown in the figure. Show that the electric field everywhere in the empty region is given by where i is the displacement vector directed from 01 to O2. 4πεο R3' (Hint: Model the sphere as a positively charged sphere with no cavity + negatively charged sphere with negative charge at the location of the cavity. Then pick a point inside the negatively charged sphere (not at its center, since you need to prove the expression is correct for anywhere inside the cavity) and use gauss's law to find the electric field due to each sphere). R
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Transcribed Image Text:A total charge Q is distributed uniformly throughout a spherical volume that is centered at 01 and has a
radius R. Without disturbing the charge remaining, charge is removed from the spherical volume that is
centered at O2, as shown in the figure. Show that the electric field everywhere in the empty region is given by
where r is the displacement vector directed from O1 to 02.
4TE,R3'
(Hint: Model the sphere as a positively charged sphere with no cavity + negatively charged sphere with
negative charge at the location of the cavity. Then pick a point inside the negatively charged sphere (not at its
center, since you need to prove the expression is correct for anywhere inside the cavity) and use gauss's law
to find the electric field due to each sphere).
02
R
Expert Solution
Step 1
Let's consider the following diagram.
Consider is the center of the entire sphere, is the center of the cavity which is at a distance from . P is an arbitrary point inside the cavity. The distance of P from is and from is .
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