2 2 x² + y² a² a. Show that when a = 1, the outward flux across the cone is zero. b. Find the outward flux (away from the z-axis), for any a > 0. Consider the field F= (x,y,z) and the cone z² = for Osz≤ 1.
2 2 x² + y² a² a. Show that when a = 1, the outward flux across the cone is zero. b. Find the outward flux (away from the z-axis), for any a > 0. Consider the field F= (x,y,z) and the cone z² = for Osz≤ 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the field \( \mathbf{F} = (x, y, z) \) and the cone \( z^2 = \frac{x^2 + y^2}{a^2} \) for \( 0 \leq z \leq 1 \).
a. Show that when \( a = 1 \), the outward flux across the cone is zero.
b. Find the outward flux (away from the z-axis), for any \( a > 0 \).
---
a. Using \( a = 1 \), write the cone as \( z = g(x, y) \).
\[ z = \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F511d779c-bf10-4315-98b1-4f0038c55113%2Faeb752a7-5299-4610-b511-3bda409f2483%2Fpd41et_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the field \( \mathbf{F} = (x, y, z) \) and the cone \( z^2 = \frac{x^2 + y^2}{a^2} \) for \( 0 \leq z \leq 1 \).
a. Show that when \( a = 1 \), the outward flux across the cone is zero.
b. Find the outward flux (away from the z-axis), for any \( a > 0 \).
---
a. Using \( a = 1 \), write the cone as \( z = g(x, y) \).
\[ z = \boxed{} \]
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