Explanation Given: The electric charge is distributed along y = x − 1 for 1 2 ≤ x ≤ 2 with charge density δ ( x , y ) = x 3 y . Formula Used: The electric potential at the point P is: V ( P ) = k ∫ C δ ( x , y , z ) r P d s Calculation: The electric charge is distributed along the curve: y = x − 1 ; 1 2 ≤ x ≤ 2 The parameterization of the given segment is: r ( t ) = ( t , t − 1 ) ; 1 2 ≤ t ≤ 2 Now, the derivative of r ( t ) is: r ' ( t ) = ( 1 , − 1 t 2 ) ‖ r ' ( t ) ‖ = 1 2 + ( − 1 t 2 ) 2 = 1 + 1 t 4 = 1 t 2 t 4 + 1 Now, the charge density function along the parameterized curve: δ ( r ( t ) ) = t 2 The distance r P from point P = ( 0 , 0 ) to a point ( t ,...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 52E

To determine

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Calculate $V (P)$ at the origin $P = (0, 0)$ .

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Chapter 17.2, Problem 51E

Chapter 17.2, Problem 53E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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