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Magnetic Induction electricity and magnetism meet! Faraday’s Law • In the 1830’s both Faraday and Henry discovered that a changing magnetic field creates a current. This can be given a precise mathematical form as: d m EMF E dl dt • This is called Magnetic Induction An Intriguing Possibility... • If changing magnetic flux can create a current, can one also conclude that a changing magnetic field can produce an electric field? • Don’t we already have evidence that the converse - a changing electric field produces a magnetic field - occurs? Examples... • Simple cases of magnetic induction • Motional EMF • Lenz’s Law: Induced EMF and induced Current oppose each other • “Back” EMF: This explains the negative sign in d EMF E dl m dt Inductance • Inductance is a property of any conductor and can be defined in terms of the concepts of current and magnetic flux by the following simple expression: m LI L is known as the self-inductance and is measured in Henries (H) Example... • Inductance of a solenoid: m NBA L I I B o ( N / l ) I Inductance in Circuits • If we run a current through a solenoid (inductor), it will produce a back emf and we can apply Kirchhoff’s Rules to account for this in a circuit: dI E0 IR L 0 dt Generators and Alternating Current • What happens if we spin a conducting loop in a magnetic field? answer… its easy to show that: E NBA Modifying old Concepts... • Root-mean-square Erms • Inductive Reactance • Capacitive Reactance 1 Emax 2 XL L 1 XC C