12. The electric potential generated by a uniformly charged disk of total charge Q and radius R is given by 2Q F(y) R2 (Vy² + R² – y), - U where y is the distance from the disk and F(y) is the potential at distance y. We want to understand what happens when y is very large, so do this: a. Change variables from y to x = 1/y, so that when y is big, x is close to zero. Simplify! b. Find a Taylor polynomial centered at x = : 0 for the potential in terms of x. c. Use this to justify the following claim: "at points far from the disk, the po- tential is approximately Q/y."
12. The electric potential generated by a uniformly charged disk of total charge Q and radius R is given by 2Q F(y) R2 (Vy² + R² – y), - U where y is the distance from the disk and F(y) is the potential at distance y. We want to understand what happens when y is very large, so do this: a. Change variables from y to x = 1/y, so that when y is big, x is close to zero. Simplify! b. Find a Taylor polynomial centered at x = : 0 for the potential in terms of x. c. Use this to justify the following claim: "at points far from the disk, the po- tential is approximately Q/y."
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Transcribed Image Text:12. The electric potential generated by a uniformly charged disk of total charge Q
and radius R is given by
20
F(y) =
(Vy² + R² – y),
-
where y is the distance from the disk and F(y) is the potential at distance y. We
want to understand what happens when y is very large, so do this:
a. Change variables from y to x = 1/y, so that when y is big, x is close to zero.
Simplify!
b. Find a Taylor polynomial centered at x = 0 for the potential in terms of x.
c. Use this to justify the following claim: "at points far from the disk, the po-
tential is approximately Q/y."
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