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

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.2, Problem 50E

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

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Chapter 17.2, Problem 49E

Chapter 17.2, Problem 51E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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