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(c) Find an algebraic expression for this force using a limiting case where d→ 0. (d) Find a more accurate algebraic approximation for this force by using a Taylor expansion.

(c) Find an algebraic expression for this force using a limiting case where d→ 0. (d) Find a more accurate algebraic approximation for this force by using a Taylor expansion.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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e Coulomb force is proportional to 1/1², but often we have multiple distances involved. Let's s have distances d and D and we know that d << D. A hypothetical Coulomb force could be wr kQq where k = 9.0 x 109 Nm²/C² and Q (and q) has units of charge, C. (D+d)²¹ |F| = (b) Show that this hypothetical Coulomb force has the correct units. (c) Find an algebraic expression for this force using a limiting case where d → 0. (d) Find a more accurate algebraic approximation for this force by using a Taylor expansion. Tips: We are looking for a better approximation than part (c). How can we write the denominator in the form (1 + x)", where x << 1? You may find it useful to use a negative value of n.
Transcribed Image Text:e Coulomb force is proportional to 1/1², but often we have multiple distances involved. Let's s have distances d and D and we know that d << D. A hypothetical Coulomb force could be wr kQq where k = 9.0 x 109 Nm²/C² and Q (and q) has units of charge, C. (D+d)²¹ |F| = (b) Show that this hypothetical Coulomb force has the correct units. (c) Find an algebraic expression for this force using a limiting case where d → 0. (d) Find a more accurate algebraic approximation for this force by using a Taylor expansion. Tips: We are looking for a better approximation than part (c). How can we write the denominator in the form (1 + x)", where x << 1? You may find it useful to use a negative value of n.
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