solutions_29 - follows: ( ) 4 3 2 2 1 2 2 aR dr r a rdr ar...

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PHY2061 R. D. Field Solutions Chapter 29 Page 1 of 2 Chapter 29 Solutions Problem 1: Wire B is three times longer than wire A , and the two wires have the same volume . If both wires are made of the same substance and if the resistance of wire A is 9 Ohms , what is the resistance of wire B ( in Ohms ). Answer: 81 Solution: We know that the resistance of a wire of length L , cross sectional area A , and resistivity ρ is given by V L A L R 2 ρ = = , where V is the volumn, V = LA . Thus, = = = = = = 81 ) 9 ( 9 9 9 ) 3 ( 2 2 2 A A A A A B B B R V L V L V L R . Problem 2: Consider a long straight cylindrical wire with radius R carrying the non- uniform current density, J(r)=ar 2 , where r is the distance from the center axis of the wire. How much total current I passes through the wire? Answer: π aR 4 /2 Solution: The current I is the &flux± associated with the current density as
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Unformatted text preview: follows: ( ) 4 3 2 2 1 2 2 aR dr r a rdr ar A d J I R R = = = = r r . Problem 3: Consider a long straight cylindrical wire with radius R = 0.1 m is carrying the non-uniform current density which points along the axis of the wire and has a magnitude, J(r) = a/r , where r is the distance from the center axis of PHY2061 R. D. Field Solutions Chapter 29 Page 2 of 2 the wire. If a = 2 A/m , how much total current I passes through the wire ( in A )? Answer: 1.26 Solution: The current I is the &flux associated with the current density as follows: A m m A aR rdr r a A d J I R 26 . 1 ) 1 . )( / 2 ( 2 2 2 = = = = = r r ....
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solutions_29 - follows: ( ) 4 3 2 2 1 2 2 aR dr r a rdr ar...

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