2. A solid sphere of radius R, centered at the origin, has a uniform positive charge density Po A solid sphere of radius R/2 centered at x = R/2 is carved out, as shown in the figure. The z-direction, coming out of the page, is understood in the figure. (a) Show that the electric field EA at an arbitrary point A (in three dimensional space) is uniform (that is, constant) inside the cavity. (b) Find the electric field Eg, at an arbitrary point B (in three dimensional space) outside the cavity but inside the large solid sphere. (Hint: Consider the superposition of the solid sphere of radius R with another solid sphere of radius R/2 with opposite sign charge density, and apply Gauss law to each, and then sum them up. In doing so, specify the position vectors carefully). B A R/2 L. 2
2. A solid sphere of radius R, centered at the origin, has a uniform positive charge density Po A solid sphere of radius R/2 centered at x = R/2 is carved out, as shown in the figure. The z-direction, coming out of the page, is understood in the figure. (a) Show that the electric field EA at an arbitrary point A (in three dimensional space) is uniform (that is, constant) inside the cavity. (b) Find the electric field Eg, at an arbitrary point B (in three dimensional space) outside the cavity but inside the large solid sphere. (Hint: Consider the superposition of the solid sphere of radius R with another solid sphere of radius R/2 with opposite sign charge density, and apply Gauss law to each, and then sum them up. In doing so, specify the position vectors carefully). B A R/2 L. 2
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Please answer both parts with detailled explanations and steps.
Transcribed Image Text:2. A solid sphere of radius R, centered at the origin, has a uniform positive charge density Po
A solid sphere of radius R/2 centered at x = R/2 is carved out, as shown in the figure. The
z-direction, coming out of the page, is understood in the figure.
(a) Show that the electric field EA at an arbitrary point A (in three dimensional space) is uniform
(that is, constant) inside the cavity.
(b) Find the electric field Eg, at an arbitrary point B (in three dimensional space) outside the
cavity but inside the large solid sphere. (Hint: Consider the superposition of the solid sphere of
radius R with another solid sphere of radius R/2 with opposite sign charge density, and apply
Gauss law to each, and then sum them up. In doing so, specify the position vectors carefully).
L.
B
A
R/2
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Step 1: Part (a)
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