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tutorial11Solution

# tutorial11Solution - The University of Western Australia...

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1 The University of Western Australia School of Electrical, Electronic and Computer Engineering Solutions - Tutorial Sheet 11, 2006 Electromagnetic Theory ENGT 3303 Question 1 (a) Write the following time varying vector fields in phasor form. i. ( ) z y t a B π ω + = cos 2 ( ) ( ) direction y negative e e e e z y j z y j j z y j s = = = + a a a B 1 2 2 2 π π π π ii. ( ) ( ) ( ) ( ) y x y x z t t z t t a a a a C + = + = ω π ω ω ω cos 8 2 / cos 5 cos 8 sin 5 y jz x y jz x j s e j e e a a a a C + = + = 8 5 8 5 2 / π positive z-direction iii. ( ) y x y x x t e x t e a a D ) 2 / 5 cos( 5 sin 2 2 π ω ω = = y x j y x j j x s je e e e a a D ) 5 2 ( 5 2 / 2 + = = π positive x-direction (b) Write the vector potential for a short dipole in phasor notation: ( ) ( ) ( ) θ β ω θ β ω θ π ω µ φ θ a a A r t r t r p t r r = cos sin cos cos 4 ) , , , ( 0 ( ) θ β β θ θ π ω µ φ θ a a A r j r r j s e e r p r = sin cos 4 ) , , ( 0 (c) Express the following phasors in instantaneous form.

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