57. A narrow, negatively charged ring of radius R exerts a force on a positively charged particle P located at distance x above the center of the ring of magnitude kx F(x): (x2 + R2)3/2 where k > 0 is a constant (Figure 12). (a) Compute the third-degree Maclaurin polynomial for F. (b) Show that F -(k/R³)x to second order. This shows that when x is small, F(x) behaves like a restoring force similar to the force exerted by a spring. (c) Show that F(x)- -k/x? when x is large by showing that F(x) lim x00 -k/x2 Thus, F(x) behaves like an inverse square law, and the charged ring looks like a point charge from far away. F(x) х Nearly linear here х Nearly inverse square here FIGURE 12
57. A narrow, negatively charged ring of radius R exerts a force on a positively charged particle P located at distance x above the center of the ring of magnitude kx F(x): (x2 + R2)3/2 where k > 0 is a constant (Figure 12). (a) Compute the third-degree Maclaurin polynomial for F. (b) Show that F -(k/R³)x to second order. This shows that when x is small, F(x) behaves like a restoring force similar to the force exerted by a spring. (c) Show that F(x)- -k/x? when x is large by showing that F(x) lim x00 -k/x2 Thus, F(x) behaves like an inverse square law, and the charged ring looks like a point charge from far away. F(x) х Nearly linear here х Nearly inverse square here FIGURE 12
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.6: Algebraic Extensions Of A Field
Problem 7E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage