A total charge of Q is distributed uniformly on a line segment of length 2L along the y axis (see figure) The x component of the electric field at a point (a, 0) is given by where k is a physical constant and a 0 a Confirm that b Letting Q 2L be the charge density on the line segment, show that if ...

a Exa cL L kQa 2L 1 L dy a y2 Thus Exa dy a y22 Exa0 L 2 2 a kQ aa L Let ...

A total charge of Q is distributed uniformly on a line segment of length 2L along the

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A total charge of Q is distributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by

kQa E,(a) = 2L dy (a² + y²)³/2* -L

where k is a physical constant and a > 0.

a. Confirm that kQ E(a) = aVa? + L?

b. Letting ρ = Q/2L be the charge density on the line segment, show that if L → ∞, then E_x(a) = 2kρ/a.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Question Posted: Apr 06, 2019 12:08 PM

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A total charge of Q is distributed uniformly on a line segment of length 2L along the

Question:

kQa E,(a) = 2L dy (a² + y²)³/2* -L kQ E(a) = aVa? + L?

Step by Step Answer:

a Exa cL L kQa 2L 1 L dy a y2 Thus Exa dy a y22 Exa0 L 2 2 a kQ aa L Let ...View the full answer

Calculus Early Transcendentals

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