solution3_calculus

solution3_calculus - EE1259 Assignment 3 (Due on Thursday,...

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EE1259: Electromagnetic assignment 1 Problem 5 Problem 6 EE1259 Assignment 3 (Due on Thursday, September 20, 2007) 1. Let R r be the distance vector from a fixed point (x’, y’, z’) to the point (x, y, z), let R to be its length. Show that a) () R R r 2 2 = b) R R a R a R R R R R / / / 1 2 3 r r r r = = = c) What is the general formula for ( ) n R 2. Compute r r a a r r , where r a r is the unit vector in spherical coordinate, or you can write ( ) 2 2 2 z y x a z a y a x a z y x r + + + + = r r r r 3. For a scalar function f and a vector function G , prove: ( ) ( ) ( ) G f G f G f r r r × + × = × 4. A vector field ρ a D r r 3 = exists in the region between two concentric cylindrical surfaces defined by =1 and =2 , with both cylinders extending between z=0 , and z=5 . Verify the divergence theorem by evaluating the following. (a). S S d D r r (b). ( ) ∫∫∫ V dv D r 5. Check the divergence theorem for the function φ θ a r a r a r v r r r r r tan cos 4 sin 2 2 2 + + = using the volume of the “ice-cream cone” shown below (the top surface is spherical with radius R and centered at the origin).
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solution3_calculus - EE1259 Assignment 3 (Due on Thursday,...

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