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Unformatted text preview: 10:2A Use radian mode for all calculations. 1. Within a certain non-conducting region m F 11 10 − = ε and m H 5 10 − = µ . If ( ) ( ) T y 10 sin t 10 cos 10 2 x ˆ 3 5 4 − − × = B r a.) Use Ampere’s Law, t D J H ∂ ∂ + = × ∇ r r r r c , to find the expression for the electric field, E r . Solution: Since the region is non-conducting and B H r r µ = and D E r r ε = , and = c J t ∂ ∂ ε = × ∇ E H r r r . Then ( ) ( ) ( ) ( ) ∫ ∫ × ∂ ∂ µε − = × ∇ µε = − − dt z ˆ y 10 sin t 10 cos 10 2 y 1 dt 1 3 5 4 B E r r r ( ) ( ) ( ) ( ) × µε = ∫ − − − dt y 10 cos t 10 cos 10 2 10 z ˆ 3 5 4 3- E r ( ) ( ) ( )( ) ( ) ∫ − − − − × = dt t 10 cos 10 10 y 10 cos 10 2 z ˆ 5 11 5 3 7- E r ( ) ( t 10 sin y 10 cos 10 10 2 z ˆ 5 3 5 9 − × − = E r ) ( ) ( ) m V t 10 sin y 10 cos 10 2 z ˆ 5 3 4 − × − = E r b.) Find the magnetic flux, Φ , in Webers, through the surface defined by...
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