To determine The point at which the entire potential energy of q is minimum. Explanation The distance between two charge is 10 mm. x 1 + x 2 = 10 x 2 = 10 − x 1 . The potential energy E of an electric charge q due to another charge q 1 at a distance of r 1 is proportional to q 1 and inversely proportional to r 1 . E ∝ q 1 r 1 E = k q 1 r 1 Where, k is the constant of proportionality. The potential energy due to charge 2 nC . E 1 = 2 k x 1 The potential energy due to charge 1 nC . E 2 = k 10 − x 1 Then total potential energy. E = E 1 + E 2 Substitute, E 1 = 2 k x 1 , E 2 = k 10 − x 1 in n = n 1 + n 2 . E = E 1 + E 2 = 2 k x 1 + k 10 − x 1 Differentiate function E with respect to x . d E d x = d d x ( 2 k x 1 + k 10 − x 1 ) = 2 k ( − 1 ) x 1 2 + k ( 10 − x 1 ) 2 = k ( 10 − x 1 ) 2 − 2 k x 1 2 For maxima and minima value of E evaluate d E d x = 0

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 24.7, Problem 44E

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The point at which the entire potential energy of q is minimum.

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Chapter 24.7, Problem 43E

Chapter 24.7, Problem 45E

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Chapter 24 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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