Download Understanding Electromagnetic Induction: Currents, Flux, and Faraday's Law - Prof. Hailu G and more Study notes Physics in PDF only on Docsity! Electromagnetic Induction Induced currents • Current creates a magnetic field. • can magnetic field create current? • Faraday’s discovery There is a current in a coil of wire if and only if the magnetic field passing through the coil is changing The Magnetic Flux • Magnetic flux is defined as cosABm SI unit – 1 weber – 1 Wb = 1 T m2 The Magnetic Flux • Let’s define an area vector to be perpendicular to the loop magnitude equal to the area A of the loop. • The magnetic flux can be written as • Nonunifom Field – Divide the loop into many small pieces of area dA. The infinitesimal flux though one such area is – The total magnetic flux though the loop BAm AdBd m looptheofarear m AdB A Lenz’s Law • There is an induced current in a closed, conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux. • The flux can be changing because – The magnetic field through the loop changes, – The loop changes in area or angle, or – The loop moves in or out of a magnetic loop. Examples • What is the magnetic flux? • The figure below shows a 10-cm-diameter loop in three different magnetic fields. The loop’s resistance is 0.20 Ω. For each case, determine the induced emf, the induced current, and the direction of the current. Induced Fields • Consider a conducting loop in a region of increasing magnetic field. • There will be induced current but what force pushes charges around the loop? • There must be an induced electric field. • Induced electric field exists even if there is no conducting loop. • It is non-coulombic electric field. • Non-conservative field. • emf is defined as • For a loop perpendicular to the magnetic field and only magnetic field changes sdEq W dt dB 2 r E dt dB AsdE Maxwell’s Theory of Electromagnetic Waves • A changing magnetic field creates an induced electric field – Faraday • A changing electric field creates an induced magnetic field. – Maxwell • Maxwell was able to predict that electric and magnetic fields would be able to sustain themselves, free from charges and currents, if they took the form of an electromagnetic wave. 00 waveem 1 v Potential Difference Across an Inductor • Since an ideal inductor has no resistance, the potential difference due to steady current is zero. • When the original current changes there will be induced current and induced emf is • Including the sign convention is dt dI L dt d dt d N mcoilpercoil dt dI LVL Energy in Inductors and Magnetic Fields • An inductor stores energy that can later be released • The energy is being transferred to the inductor at the rate • Using solenoid as an example, • The magnetic field energy density is dt dI LIVIP Lelec 2 I 0 L L LI 2 1 'dI'ILU dt dI LI dt dU 2 0 L AlB2 1 U 2 0 B B2 1 u LC Circuits • Consider the circuit shown with initial charge Q0, and inductor, switch Examples • A solenoid inductor has an emf of 0.20 V when the current through it changes at the rate 10.0 A/s. A steady current of 0.10 A produces a flux of 5.0 μWb per turn. How many turns does the inductor have? • An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the capacitance? Examples • The switch in the figure below has been open for a long time. It is closed at t = 0 s. – What is the current through the battery immediately after the switch is closed? – What is the current through the battery after the switch has been closed a long time?
