-yi+ xj2. Find the flux of F =across the curve C given by r(t) = a cos(t)i+a sin(t)j,x2 + y2for 0

∵ Given thatF=-yi^+xj^x2+y2; 0≤t≤2π r(t)=acosti^+asintj^ As we know that Flux=∬ F·nds…

Answered: yi + aj 2. Find the flux of F = across…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

-yi+ xj
2. Find the flux of F =
across the curve C given by r(t) = a cos(t)i+a sin(t)j,
x2 + y2
for 0 <t< 27.

Expert Solution

Step 1

$∵ G i v e n t h a t F = \frac{- y \hat{i} + x \hat{j}}{\sqrt{x^{2} + y^{2}}}; 0 \leq t \leq 2 π r (t) = acos (t) \hat{i} + asin (t) \hat{j}$

As we know that Flux $= \iint F \cdot n d s$

Since given $r (t) = a \cos (t) \hat{i} + a \sin (t) \hat{j} \Rightarrow x (t) = a \cos (t), y (t) = a \sin (t) F (x, y) = \frac{- y}{\sqrt{x^{2} + y^{2}}} \hat{i} + \frac{x}{\sqrt{x^{2} + y^{2}}} \hat{j} F (r (t)) = \frac{- a \sin (t)}{\sqrt{a^{2} \cos^{2} (t) + a^{2} \sin^{2} (t)}} \hat{i} + \frac{a \cos (t)}{\sqrt{a^{2} \cos^{2} (t) + a^{2} \sin^{2} (t)}} \hat{j} F (r (t)) = \frac{- a \sin (t)}{a} \hat{i} + \frac{a \cos (t)}{a} \hat{j} F (r (t)) = - \sin (t) \hat{i} + \cos (t) \hat{j}$