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Unformatted text preview: Solution Derivations for Capa #9 1) Assume that a lightning bolt can be represented by a long straight line of current. If 15 . C of charge passes by in a time of 1 . 5 10 3 s , what is the magnitude of the magnetic field at a distance of 28 . m from the bolt? Q = Given t = Given r = Given Current is defined to be I = dQ dt . We know that a total charge of Q passed by in a time t , so the current is I = Q t . The magnetic field of an infinite line is given by B = I 2 r = Q 2 rt 2) A small diameter, 21 cm long solenoid has 263 turns and is connected in series with a resistor and battery. The size of the magnetic field inside the solenoid is 6 . 662 10 4 T when a voltage of 80 . V is applied to the circuit. Calculate the resistance of the circuit. Use units of Ohm. l = Given N = Given B = Given V = Given R = ? The Bfield of a solenoid is given by B = nI = NI l where the last step follows since n = N l . From Ohms Law, I = V R Thus, B = NV lR So, R = NV lB 3) The wire in the above figure carries a current I which travels into the paper. North is up, East is right, etc. (For each statement select T True, F False). WARNING: you have only 4 tries. 1 QUESTION: A) The magnetic field at p 1 points east. B) The magnetic field at p 1 points south. C) The magnetic field at p 1 points out of the paper. ANSWER: A) False, Use the right hand rule. Point your thumb in the direction of I, your fingers will curl in the direction of B. It is south. B) True, See (A) C) False, See (A) 4) If the magnetic field at point p 1 is 2 . 5 tesla, what is the magnetic field at p 2 ? B p 1 = Given B p 2 = ? The magnetic field due to a long, straight wire is B = I 2 r We are told this field at point p 1 . B p 1 = I 2 r At point p 2 , the distance r is twice that at p 1 . Thus, B p 2 = I 2 (2 r ) = 1 2 I 2 r = 1 2 B p 1 5) In the figure below, the bottom wire carries a current of 4 . A . The current of the upper wire is directed in the opposite direction, and the total magnetic field at point p 1 is zero. What is the current in the top wire? I 2 = Given B p 1 = Given (0) Since we know the field at p 1 , we can find other unknowns. Equating the field due to each wire at p 1 and setting the equations equal to each other, B 2 = I 2 2 a B 1 = I 1 2 (3 a ) 2 Thus, I 2 2 a = I 1 2 (3 a ) I 2 = I 1 3 I 1 = 3 I 2 6) Given that the wires are separated by 2 a , where a = 0 . 021 m , what is the magnitude of the magnetic field at point p 2 ?...
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This homework help was uploaded on 04/03/2008 for the course PHYS 1120 taught by Professor Rogers during the Fall '08 term at Colorado.
 Fall '08
 ROGERS
 Physics, Charge, Current, Light

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