Homework-5-Solutions

Homework-5-Solutions - ECE 305 (Fall 2008) Homework 5...

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ECE 305 (Fall 2008) Page 1 of 1 Homework 5 Assigned : Wednesday October 8, 2008 Due : Start of class on October 15, 2008 1. Show that 3 1' ' ' ⎛⎞ ∇= ⎜⎟ ⎝⎠ rr , and 3 ' ' . Note: is the derivative with respect to the primed coordinates. 2. Text problem 4.17. 3. Text problem 4.20. 4. Text problem 4.19 5. Text problem 4.24. 6. Text problem 4.31.
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1. Let ˆˆ ˆ x xy yz z =++ r and ˆ x z ′′ r . Then, () ( ) ˆ x xx y yy z zz −= − + − +− rr and 22 2 1 2 2 xx yy zz ′′′ −= − +− +− ⎡⎤ =− + + ⎣⎦ Since ˆ x x φ φφ ∂∂∂ ∇= + + , consider ( )( ) ( ) ( ) 1 2 2 3 2 2 3 2 2 1 1 2 2 xx xx ⎛⎞ ∂∂ + + ⎜⎟ ∂− ⎝⎠ + + −+ Similarly, ( ) 3 2 2 1 y ( ) 3 2 2 1 z Thus, 3 2 2 3 2 2 3 2 2 111 1 ˆ ˆ ˆ ˆ xyz xxx yyy zzz ⎛⎞⎛⎞⎛⎞⎛⎞ + + ⎜⎟⎜⎟⎜⎟⎜⎟ −∂ ⎝⎠⎝⎠⎝⎠⎝⎠
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Homework-5-Solutions - ECE 305 (Fall 2008) Homework 5...

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