Download Lecture 28: Electromagnetic Induction - Flux, Faraday's Law, and Lenz's Law and more Lecture notes Classical Physics in PDF only on Docsity! PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 81 N S θ B A Summary of Lecture 28 – ELECTROMAGNETIC INDUCTION 1. Earlier we had defined the flux of any vector field. For a magnetic field, this means that flux of a uniform magnetic field (see figure) is cos . If the field is not constant ove B A BA θ⊥Φ = = 2 r the area then we must add up all the little pieces of flux: . The dimension of flux is magnetic field area, and the unit is called weber, where 1 weber 1 tesla metre . B B dAΦ = ⋅ × = ⋅ ∫ 2. A fundamental law of magnetism states that the net flux through a closed surface is always zero, 0. Note that this is very different from what you learned earlier in electrostati B B dAΦ = ⋅ =∫ cs where the flux is essentially the electric charge. There is no such thing as a magnetic charge! What we call the magnetic north (or south) pole of a magnet are actually due to the particular electronic currents, not magnetic charges. In the bar magnet below, no matter which closed surface you draw, the amount of flux leaving the surface is equal to that entering it. A sphere of radius is placed near a long, straight wire that carries a steady current . The magnetic field generated by the current is . Find the total magnetic flux passing thro R I B Example : ugh the sphere. docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 82 B Answer: zero, of course! 3. Faraday's Law for Induced EMF: when the magnetic flux changes in a circuit, an electro- motive force is induced which is proportional to the rate of change of flux. Mathematically, where is the induced emf. If the coil consists of turns, then . How does th B Bd dN N dt dt ε ε εΦ Φ= − = − e flux through a coil change? Consider a coil and magnet. We can: a) move the magnet, b) change the size and shape of the coil by squeezing it, c) move the coil. In all cases, the flux through the coil changes and is non-zero leading to an induced emf. : A flexible loop has a radius of 12cm and is in a magnetic field of strengt Bd dt Φ Example h 0.15T. The loop is grasped at points A and B and stretched until it closes. If it takes 0.20s to close the loop, find the magnitude of the average induced emf in it during this time. Solu 2 tion: Here the loop area changes, hence the flux. So the induced emf is: final flux initial flux 0 (0.12) 0.15 0.034 Volts. time taken 0.2 Bd dt πε ⎡ ⎤Φ − − ×⎡ ⎤= − ≈ − = − =⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦ A wire loop of radius 0.30m lies so that an external magnetic field of +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. Find the magnitude of the aver Example : 2 age induced EMF in the loop during this time. Solution: Again, we will find the initial and final fluxes first and then divide by the time taken for the change. Use to calculBA B rπΦ = = 2 2 2 2 ate the flux. 0.30 (0.30) 0.085 Tm 0.20 (0.30) 0.057 Tm 0.085 0.057 0.095 V 1.5 i f f i t t π π ε Φ = × × = Φ = − × × = − Φ −ΦΔΦ − = = = = Δ Δ docsity.com
