Quiz (Line Integrals)

Show all work and justify each step.

(1) Evaluate the line integral where and is the boundary of the triangle with vertices and , transversed once clockwise, as viewed from above.

(2) A 5,000-lb satellite orbits the earth in a circular orbit 5,000 mi from the center of the earth. How much work is done as the satellite moves through one complete revolution?

(3) Suppose a particle with charge and mass moves with velocity under the influence of an electric field and a magnetic field Then the total force on the particle is called the Lorentz force. Use Newton's second law of motion, to show that



and then evaluate the line integral where is the trajectory of a particle raleving with constant speed.  

(4) Let and let and be the following two paths joining to

   and   

Show that Explain what this means?

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Cite this as:
Line Integrals Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/line-integrals-quiz.html