Phys17

# Phys17 - Unit 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8...

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1 Unit 17 Electrodynamics II 17.1 Ampere’s law 17.2 Forces between current wires 17.3 Magnetism 17.4 Induced EMF 17.5 Magnetic flux 17.6 Faraday’s law of induction 17.7 Lenz’s law 17.8 Motional EMF 17.1 Ampere’s law Electric currents can create magnetic fields. The direction of the magnetic field is given by the magnetic field right-hand rule. The magnetic field right-hand rule states the following: To find the direction of the magnetic field due to a current- carrying wire, point the thumb of your right hand along the wire in the direction of the current I. Your fingers are now curling around the wire in the direction of the magnetic field. Experiments show that the field produced by a current-carrying wire doubles if the current I is doubled. In addition, the field decreases by a factor of 2 if the distance from the wire, r , is doubled. Hence, we conclude that the magnetic field B must be proportional to r I / ; that is r I B . Ampere’s law states that the sum of l d B G G along the closed path is proportional to the current enclosed by the path. Mathematically, we have enclosed I l d B 0 µ = G G . The proportional constant, 0 is the permeability of free space. Its value is A m T / 10 4 7 0 × = π . For example, the magnetic field at a distance r due to a long wire of current can by obtained by the Ampere’s law.

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2 enclosed I r B l d B 0 ) 2 ( µ π = = G G , which gives r I B 2 0 = . Remark: Recall that in the long solenoid, which has n turns per unit length of solenoid and carries a current I , the magnetic field B at a point O on the axis of solenoid is found to be nI B 0 = . In fact, this expression can be obtained simply by using the Ampere’s law. Consider the amperian loop as shown in figure. The length, side 1 of the amperian loop is L , which has N turns of coils. The magnetic field is nearly uniform and tightly packed inside the loops. In the ideal case of a very long, tightly packed solenoid, the magnetic field outside is practically zero – especially when compared with the intense field inside the solenoid. We can use this idealization, in combination with Ampere’s law, to calculate the magnitude of the field inside the solenoid. enclosed side side side side I BL L B L B L B L B l d B 0 4 // 3 // 2 // 1 // 0 0 0 = + + + = + + + = G G The answer is simply ) ( 0 0 nL I IN BL = = , which gives nI B 0 = . Example If you want to increase the strength of the magnetic field inside a solenoid is it better to (a) double the number of loops, keeping the length the same, or (b) double the length, keeping the number of loops the same? Answer: Since nI B 0 = , we know that the number of coil per unit length of solenoid governs the magnitude of magnetic field. Doubling the number of loops and keeping the length the same, results in doubling the variable n . So, the answer is (a).
3 Example Two wires separated by a distance of 22 cm carry currents in the same direction. The

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## This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.

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Phys17 - Unit 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8...

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