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Unformatted text preview: Electromagnetics HW.10 Group.3 Deadline 5 / 10 / 89 1. In this problem we want to find the magnetic energy in the most general form, suppose that there are n loops of current, i ( t ) = ( i 1 ( t ) i 2 ( t ) ... i n ( t )) T , which have the steady amounts of I = ( I 1 I 2 ... I n ) T . Use the equation Φ( t ) = Li ( t ) and V ( t ) = L di ( t ) dt , which Φ is the magnetic flux and L is the matrix of inductance to show that W m = 1 2 n X i =1 n X j =1 L ij I i I j 2. A long coaxial cable carries current I (the current flows down the surface of the inner cylin- der, radius a , and back along the outer cylinder, radius b ). a) Find the magnetic energy stored in a section of length l . b) Use the equation W m = 1 2 LI 2 to find the self inductance. 3. Find the mutual inductance of a long wire carries current I 1 and the the loop ABCD which has the current I 2 . Also calculate the term caused by the mutual energy stored in the system.(hint: ∇ ....
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- Fall '10