a. Using AV = V(rf) – V(ri) : = ri – SE · dr determine the electric potential as a function of distance r from the center of the sphere for points outside the sphere r > R. Be sure to draw a diagram and label any quantities of interest. (Hint: Remember that V = 0 at r = ∞ so you will want to integrate from r = ∞ to rf = r. See page 716 of the text if you are having trouble.) b. Repeat this calculation for points inside the sphere r ≤ R. Be sure to draw a diagram and label any quantities of interest. (Hint: You need to integrate from r;= ∞ to rf = r, but remember that È has different values inside and outside the sphere.) C. Make a plot of V versus r and E versus r and note any similarities and/or Are there locations where E = 0 but V is nonzero? Explain. differences. dv d. Using E= -V - = - verify that you can get back the expression for E from dr the result of part a. dv e. Using E= -√V : = - verify that you can get back the expression for E from dr the result of north - -

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Chapter1: Units, Trigonometry. And Vectors
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Suppose you have a solid sphere of total charge Q and radius R with uniform charge density p.
Let r represent distances from the center of the sphere.
a.
Using AV = V(rf) – V(r;) =
-
=
ri
– SĒ · dr determine the electric potential as a
function of distance r from the center of the sphere for points outside the sphere r > R. Be sure
to draw a diagram and label any quantities of interest.
(Hint: Remember that V = 0 at r = ∞o so you will want to integrate from r₁ = ∞o torf = r. See
page 716 of the text if you are having trouble.)
b.
Repeat this calculation for points inside the sphere r ≤ R. Be sure to draw a
diagram and label any quantities of interest.
(Hint: You need to integrate from r; = ∞ to rƒ = r, but remember that E has different values
inside and outside the sphere.)
C.
Make a plot of V versus r and E versus r and note any similarities and/or
differences. Are there locations where E = 0 but V is nonzero? Explain.
dv
d.
Using Ē= -√V =
✩ verify that you can get back the expression for È from
dr
the result of part a.
dv
e.
Using Ē = -VV
✩ verify that you can get back the expression for E from
dr
the result of part b.
=
Transcribed Image Text:Suppose you have a solid sphere of total charge Q and radius R with uniform charge density p. Let r represent distances from the center of the sphere. a. Using AV = V(rf) – V(r;) = - = ri – SĒ · dr determine the electric potential as a function of distance r from the center of the sphere for points outside the sphere r > R. Be sure to draw a diagram and label any quantities of interest. (Hint: Remember that V = 0 at r = ∞o so you will want to integrate from r₁ = ∞o torf = r. See page 716 of the text if you are having trouble.) b. Repeat this calculation for points inside the sphere r ≤ R. Be sure to draw a diagram and label any quantities of interest. (Hint: You need to integrate from r; = ∞ to rƒ = r, but remember that E has different values inside and outside the sphere.) C. Make a plot of V versus r and E versus r and note any similarities and/or differences. Are there locations where E = 0 but V is nonzero? Explain. dv d. Using Ē= -√V = ✩ verify that you can get back the expression for È from dr the result of part a. dv e. Using Ē = -VV ✩ verify that you can get back the expression for E from dr the result of part b. =
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