374bhw5 - HW#5 —Phys374—Spring 2007 Prof Ted Jacobson...

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Unformatted text preview: HW#5 —Phys374—Spring 2007 Prof. Ted Jacobson Due before class, Friday, March 2, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374b/ [email protected] 1. Derive the identity ∇ × ( f v ) = ∇ f × v + f ∇ × v (1) where f is a scalar field and v is a vector field. [5 pts.] 2. It was claimed in class Friday that if f is a function of one variable, and if h is a function of position r , then ∇ f ( h ) = f ( h ) ∇ h . Show explicitly that this is true, by showing that the vector components of each side of the equation are equal. [5 pts.] 3. Evaluate the expression ∇ × ( f ( r ) r ) , (2) where r is the position vector from the origin to the point r , and r = | r | , using (i) Cartesian coordinates and (ii) spherical coordinates (cf. (7.16)). [3+2=5 pts.] 4. Problem 7.2 (d) only. Do this using (i) Cartesian coordinates, as indicated in the problem, and (ii) cylindrical coordinates, using (7.17). (Note that in this and the next two problems r is the cylindrical radius.) [3+2=5 pts.]is the cylindrical radius....
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