Faraday's Law and Induced Electricity: Lecture 16 in Physics 212, Study notes of Physics

Download Faraday's Law and Induced Electricity: Lecture 16 in Physics 212 and more Study notes Physics in PDF only on Docsity! Physics 212 Lecture 16, Slide 1 Physics 212 Lecture 16 Φ ⋅ = −∫ B dE dl dt Faraday’s Law 0 10 20 30 40 Physics 212 Lecture 16, Slide 2 Comment on your clicker Score Participation: Means that you participate during the whole class. - “Whole” really means 75% so you can usually miss 1 or 2 and still get your participation point. - If you answer only half of the questions you will not get a participation point that day. Extra credit: You also will get an additional .2 points per correct answer up to a maximum of 1 extra point The maximum score per lecture is 2. Physics 212 Lecture 16, Slide 5 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B A In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. There are many ways to change this… Think of Φ B as the number of field lines passing through the surface Flux: B B dAΦ = ⋅∫ Physics 212 Lecture 16, Slide 6 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B B dAΦ = ⋅∫ B A In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. Change the B field Physics 212 Lecture 16, Slide 7 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B B dAΦ = ⋅∫ B A In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. Move loop to a place where the B field is different Physics 212 Lecture 16, Slide 10 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B B dAΦ = ⋅∫ B A In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. Rotate the loop Physics 212 Lecture 16, Slide 11 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B B dAΦ = ⋅∫ In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). I Demo Physics 212 Lecture 16, Slide 12 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law In Practical Words: 1) When the flux Φ B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. B B dAΦ = ⋅∫ I Physics 212 Lecture 16, Slide 15 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law B B dAΦ = ⋅∫ B A Move loop to a place where the B field is different Same idea in our other examples: Induced dΦ/dt Physics 212 Lecture 16, Slide 16 Bdemf E dl dt Φ = ⋅ = −∫Faradays Law Executive Summary: B B dAΦ = ⋅∫ emf→current→field a) induced only when flux is changing b) opposes the change Physics 212 Lecture 16, Slide 17 0 10 20 30 40 50 60 1) A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out of the field on the right side. CD emf is defined as the change in flux in the loop, so as the loop enters the constant field, the flux increases, so the flux changes, however once it fully enters the field, it does not change any longer, so the emf becomes zero, similarly when it leaves, it has an EMF in the opposite direction because flux is Decreasing now. Physics 212 Lecture 16, Slide 20 0 10 20 30 40 50 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet. Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A a > g B a = g C a < g (copper is not ferromagnetic) Physics 212 Lecture 16, Slide 21 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet. There will be an induced current in the loop which will create a magnetic field which opposes the existing one. Therefore, our new induced magnetic field points down. It will create a situation whereby the loop will experience and upward force, slowing its rate of descent. Demos Physics 212 Lecture 16, Slide 22 Calculation • Conceptual Analysis – Once loop enters B field region, flux will be changing in time – Faraday’s Law then says emf will be induced • Strategic Analysis – Find the emf – Find the current in the loop – Find the force on the current y x v0 a b x x x x x x x x x x x x x x x x x x x x x x x x x x x x BA rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. What is the direction of the force on the loop when half of it is in the field? Physics 212 Lecture 16, Slide 25 What is the direction of the net force on the loop just after it enters the field? (A) +y (B) -y (C) +x (D) -x • Force on top and bottom segments cancel (red arrows) • Force on right segment is directed in –x direction. Force on a current in a magnetic field: F IL B= × x y v0a b x x x x x x x x x x x x x x B I Calculation y x v0 a b x x x x x x x x x x x x x x x x x x x x x x x x x x x x BA rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. Bdemf dt Φ = Physics 212 Lecture 16, Slide 26 x y v0a b x x x x x x x x x x x x x x B IF 04F aBv R= What is the magnitude of the net force on the loop just after it enters the field? (A) (B) (C) (D)2 0F a Bv R= 2 2 0 /F a B v R= 2 2 2 0 /F a B v R= ε = Bav0 0BavI R R ε = = 2 2 0 0Bav a B vF aB R R ⎛ ⎞= =⎜ ⎟ ⎝ ⎠ Calculation y x v0 a b x x x x x x x x x x x x x x x x x x x x x x x x x x x x BA rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. ILB F IL B= × F ILB= L B⊥since Bdemf dt Φ = F IL B= ×