Electromagnetic induction

Important factors in inducing currents 1.An emf is induced if the coil or the magnet (or both) move (change in flux). 2.The size of the induced emf depends on the speed of movement. 3.The induced emf depends on the strength of the B field. 4.Changing the area inside the magnetic field 5. Increasing the number of turns also changes the flux linkage, and so induces a greater emf.

What you are going to learn today What is magnetic flux, and magnetic flux linkage? What must happen to a conductor (or to the magnetic field in which it’s placed) for electricity to be generated? What factors would cause the induced emf to be greater? What is Lenz’s law and what are the applications of this law?

Flux - The rate of flow of energy through a given surface flux density B (The strength of your magnetic field) magnetic flux, .  rea  Flux Linkage, N  –(N = number of turns)

Lenz’s Law Lenz’s Law states that the direction of the induced current is always such as to oppose the change that causes the current. To include this idea in our formula, a minus sign has to be introduced, giving; Emf = – N x d  /dt

Fleming's Right hand rule

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Inducing an Emf (no current yet) Connect the coil of wire to the micro- voltmeter and place it close to the magnet. 1. Move the magnet next to the coil. What happens? How does it depend on speed and direction of movement? 2.Move the coil next to the magnet. What happens? How does it depend on speed and direction of movement? 3. Gradually unwind the coil in the magnetic field. What happens? 4. Take the coil and crumple it up, keeping it in the field. What happens?

Conductor in a magnetic field Metal rod, length L in a magnetic field moving with a velocity v down the page. An electron in the rod will experience a force (= Bev) that will push it towards the end Q The electrons will be pushed towards end Q leaving end p more positive an electric field E builds up until the force on electrons in the rod due to this electric field (= Ee) balances the force due to the magnetic field. Ee = Bev so E =Bv For a rod of length L, E = V/L and so V/L = Bv Hence the induced emf = BLv v = velocityE = Electric field V = VoltageB = Magnetic field

Completing the circuit The emf will now cause a current to flow in the external resistor R. This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left L is now the separation of the two conductors along which the rod PQ moves.) An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed. The work done in moving the rod will equal the energy dissipated in the resistor. In a time t, the rod moves a distance d = v t Work done (FxD) on the rod = BIL v t Energy dissipated in R = power x time = ItV giving BIL v t = ItV Emf (V) = BvL

However! You are increasing the area inside the magnetic field Emf (V) = BvL In one second the area has increased by Lv(A =Lv) induced emf = B x area swept out per second = B x A / t B x A can be called the magnetic flux, . Thus induced emf =  / t = rate of change of magnetic flux And more generally emf = d  / dt So how can you increase the induced voltage? L

Flux Linkage (N  ) Increasing the number of turns of wire N in our circuit increases the emf produced induced emf = rate of change of flux linkage emf = N x d  /dt

Sketching Flux Patterns