Explanation Given: p ( x ) = x ( x 2 + 1 ) − 2 × 10 − 4 C / c m for 0 ≤ x ≤ 10 Calculation: Total charge distributed is given by linear charge density*length. We have been given that, length of the glass tube = 6cm and linear charge density = p ( x ) = x ( x 2 + 1 ) − 2 × 10 − 4 C / c m which varies from 0 to 10. Therefore, total charge, C in coulombs(C) = integral of linear charge density p(x) C/cm C = ∫ 0 10 p ( x ) d x ∴ C = ∫ 0 10 x ( x 2 + 1 ) − 2 × 10 − 4 d x ∴ C = 10 − 4 ∫ 0 10 x ( x 2 + 1 ) 2 d x L e t , u = x 2 + 1 d u = 2 x d x ∴ x d x = d u 2 ∴ C = 10 − 4 ∫ 0 10 1 u 2 d u 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 28E

To determine

To find: the total charge distribute along a glass tube of length 10 cm with linear charge density $p (x) = x {(x^{2} + 1)}^{- 2} \times 10^{- 4}$ coulombs per centimeter(C/cm) for $0 \leq x \leq 10$

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Chapter 6.2, Problem 27E

Chapter 6.2, Problem 29E

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Chapter 6 Solutions

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the total charge distribute along a glass tube of length 10 cm with linear charge density p ( x ) = x ( x 2 + 1 ) − 2 × 10 − 4 coulombs per centimeter(C/cm) for 0 ≤ x ≤ 10

Solution Summary: The author calculates the total charge distributed along a glass tube of length 10 cm with linear charge density p (x ) = x(x 2 + 1) 2 10 4 coulombs per cent

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To find: the total charge distribute along a glass tube of length 10 cm with linear charge density $p (x) = x {(x^{2} + 1)}^{- 2} \times 10^{- 4}$ coulombs per centimeter(C/cm) for $0 \leq x \leq 10$

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Chapter 6 Solutions

the total charge distribute along a glass tube of length 10 cm with linear charge density p ( x ) = x ( x 2 + 1 ) − 2 × 10 − 4 coulombs per centimeter(C/cm) for 0 ≤ x ≤ 10

Solution Summary: The author calculates the total charge distributed along a glass tube of length 10 cm with linear charge density p (x ) = x(x 2 + 1) 2 10 4 coulombs per cent

Concept explainers

Videos

To find: the total charge distribute along a glass tube of length 10 cm with linear charge density p(x)=x(x2+1)−2×10−4 coulombs per centimeter(C/cm) for 0≤x≤10

Want to see the full answer?

Chapter 6 Solutions

To find: the total charge distribute along a glass tube of length 10 cm with linear charge density $p (x) = x {(x^{2} + 1)}^{- 2} \times 10^{- 4}$ coulombs per centimeter(C/cm) for $0 \leq x \leq 10$