Ch 30 Sol spr 08

# Ch 30 Sol spr 08 - INDUCTANCE 30 B1 30.4.IDENTIFY Changing...

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I NDUCTANCE 30.4.I DENTIFY : Changing flux from one object induces an emf in another object. (a) S ET U P : The magnetic field due to a solenoid is 0 . B nI E XECUTE : The above formula gives 7 4 1 4 10 T m/A (300)(0.120 A) =1.81 10 T 0.250 m B The average flux through each turn of the inner solenoid is therefore 4 2 8 1 1.81 10 T (0.0100 m) = 5.68 10 Wb B B A (b) S ET U P : The flux is the same through each turn of both solenoids due to the geometry, so 2 ,2 2 ,1 1 1 B B N N M i i E XECUTE : 8 5 (25) 5.68 10 Wb 1.18 10 H 0.120 A M (c) S ET U P : The induced emf is 1 2 . di M dt   E E XECUTE : 5 2 1.18 10 H (1750 A/s) 0.0207 V     E E VALUATE : A mutual inductance around 5 10 H is not unreasonable. 30.9. I DENTIFY and S ET U P : Apply / . L di dt E Apply Lenz’s law to determine the direction of the induced emf in the coil. E XECUTE : (a) 3 ( / ) (0.260 H)(0.0180 A/s) 4.68 10 V L di dt E (b) Terminal a is at a higher potential since the coil pushes current through from b to a and if replaced by a battery it would have the terminal at . a E VALUATE : The induced emf is directed so as to oppose the decrease in the current. 30.11. I DENTIFY and S ET U P : Use Eq.(30.6) to relate L to the flux through each turn of the solenoid. Use Eq.(28.23) for the magnetic field through the solenoid. E XECUTE : . B N L i If the magnetic field is uniform inside the solenoid . B BA From Eq.(28.23), 0 0 0 so . B N NiA B ni i l l Then 2 0 0 .

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