Explanation Given: Charge is distributed along the spiral with polar equation r = θ , 0 ≤ θ ≤ 2 π . The charge density is δ ( r , θ ) = r (assume distance is in centimeters and charge in units of 10 − 6 C/cm ). Calculate: It is given that the polar equation of the spiral is: r = θ , 0 ≤ θ ≤ 2 π A curve C in polar form r = f ( θ ) is parameterized by r ( θ ) = ( f ( θ ) cos θ , f ( θ ) sin θ ) . Thus, the spiral is parameterized by r ( θ ) = ( θ cos θ , θ sin θ ) using the result obtained in 56a. The charge density is given: δ ( r , θ ) = r From the problem 56(a) we get: ‖ r ' ( θ ) ‖ = f ( θ ) 2 + f ' ( θ ) 2 So, in this case ‖ r ' ( θ ) ‖ = θ 2 + 1 2 ( r = f ( θ ) = θ ) = θ 2 + 1 The total charge on the spiral using the line integral is: ∫ C δ ( r , θ ) d s =

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.2, Problem 61E

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The total charge.

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Chapter 17.2, Problem 60E

Chapter 17.2, Problem 62E

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The total charge.

Solution Summary: The author calculates the total charge using the polar equation r = .

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Chapter 17 Solutions

To calculate:

The total charge.