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# Physics II Elec & Magnetism CPHY 122

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This 3 page Class Notes was uploaded by Alexandria Gutkowski on Monday October 5, 2015. The Class Notes belongs to CPHY 122 at Clark Atlanta University taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/219535/cphy-122-clark-atlanta-university in Physics 2 at Clark Atlanta University.

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Date Created: 10/05/15

CPHY 122 Class Notes 14 Instructor H L Neal 1 Self Inductance Consider a single circuit around which a current I will ow after the switch is closed This current generates a magnetic eld B which gives rise to a magnetic flux gt3 through the circuit We expect the flux gt3 to be directly proportional to the current I given the linear nature of the laws of magnetostatics and the de nition of magnetic ux Thus we can write 3 LI where the constant of proportionality L is called the self inductance of the circuit 1f the current owing around the circuit changes with time then according to Faraday s law an emf 5L77 Thus the emf generated around the circuit due to its own current is directly proportional to the rate at which the current changes Lenz s law and common sense demand that if the current is increasing then the emf should always act to reduce the current and vice versa This is easily appreciated since if the emf acted to increase the current when the current was increasing then we would clearly get an unphysical positive feedback effect in which the current continued to increase without limit The self inductance L of a circuit is necessarily a positive number 2 Example 1 Here we will analyze carefully the in uence of the self inductance L in the circuit above after the switch is closed Applying Kirchoff s rules gives LIR or d IRLE The solution to this equation is found in two steps First we not that the steady state solution is steady Second we obtain the homogeneous solution by solving dI IR L7 0 l dt Note that we may write d i Ldt I R 39 lntegrating both sides gives L l I fit C n R so that L I C fit lt R Then 13 steady homo 5 L E Cexp i t At t 0 I 0 i 5 C i 0 L R L 7 so that 5 C if R Therefore 3 Mutual inductance Consider two arbitrary current loops or circuits labelled l and 2 Suppose that 1 is the instantaneous current owing around loop 1 This current generates a magnetic eld Bl which links the second circuit giVing rise to a magnetic ux 32 through that circuit lfthe current 1 doubles then the magnetic eld Bl doubles in strength at all points in space so the magnetic ux 32 through the second circuit also doubles This conclusion follows from the linearity of the laws of magnetostatics plus the de nition of magnetic ux Furthermore i is obvious that the ux t ough th around the rst circuit is zero It follows that the ux 32 through the second circuit is directly proportional to the current 1 owing around the rst circuit Hence we can write econd circuit is zero whenever the current owing 132 M2111 where the constant of proportionality M21 is called the mutual inductance of circuit 2 With respect to circuit 1 Similar e ux 31 through the rst circuit due to the instantaneous current 2 owing around the second circuit is directly proportional to that current so we can write 131 M1212 where M12 is the mutual inductance of circuit 1 with respect to circuit 2 It is possible to demonstrate mathematically that M12 M21 In other words the ux linking circuit 2 when a certain current ows around circuit 1 is exactly the same as the ux linking circuit 1 when

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