Chapter 28 - Magnetic Induction

Chapter 28 - Magnetic Induction Inducing EMF. Here, instead of V, we will use ℰ. Recall that EMF is not really a force, but is rather a voltage. Recall that magnetic fields are created by one of two things: 1. a current or 2. a changing electric field. When a capacitor charges, initially, an imaginary current is created between the two plates since it acts like there is no break. Really, a magnetic field is caused by the changing electric field between the plates. Faraday's Law - a changing magnetic current creates an electric field (or an EMF). Recall . the negative is due to lenz's law (below) Take note that can change one of two ways: 1. Change in the magnetic field: . Examples: pushing a magnet into a wire coil, or turning an electromagnet on or off. 2. Change in the area: . Examples: spin a wire coil in a magnetic field, so angle between the area vector and the magnetic field vector keeps changing. Special case: moving a wire so that it cuts a magnetic field. This also generates an EMF. Here, we have a wire of length . Note that traveling with velocity is the distance traveled, and that through a magnetic field is the area swept out by the wire. (if everything is at right angles) If not: Lenz' Law - an induced current flows in such a way as to oppose the change that caused it. If the flux is increasing, the induced current will create a magnetic field that goes against the increasing magnetic field. If the flux is decreasing, the induced current will create a magnetic field that goes with the increasing magnetic field. Examples: Pushing a magnet into a loop will cause repulsion. Pulling it out will cause attraction. (It's pretty much a specific application of the conservation of energy). Eddy Currents - (bulk conductor and changing magnetic field). When inserting a conducting block into a region with a magnetic field, charges are separated in the section intersecting the magnetic field. The voltage causes the charges to flow around the other part of the block (the part that doesn't have any magnetic field lines piercing it). When the block is at a place where the magnetic field covers the entire block, no eddy current occurs (only separation of charge occurs). These eddy currents dissipate energy as heat and flow as to oppose the motion. Induced Electric Field - since and , we get an alternate form of Faraday's Law: There is a negative because of Lenz' Law (applied to the equation after the fact) . Integrate the electric field across a closed loop. Enclose the magnetic flux that you're talking about. If the path of integration is a conduction loop, the electric field will do the work to move the charges for an induced current, not the magnetic field. The electric field is parallel to the EMF. This energy transfer is NOT conservative. The work done by the electric field is typically dissipated as heat or transferred as kinetic energy in a way that it is not reversible. Inductance ( ) - How much a coil resists changes in current, due to magnetic effects. SI Unit: Henry (H). It's an effect of Lenz' law. Causes a reverse EMF (ℰ) when you turn the circuit on (when the current changes). Definition: Magnetic Energy 1. Electromagnets store energy. When you turn a circuit on with an inductor, the magnetic field starts expanding around it. Field lines expanding cut the coil, inducing a reverse emf: this acts like a temporary resistor in the coil. Once a magnetic field is stable, reverse emf disappears. The coil looks like a wire again. When you switch the current off, the collapsing field induces an emf that tries to keep the current flowing, opposes the collapse of the field. 2. Inductor - a wire coil used in a circuit. The creation/destruction of the field acts like a break on the charges to the circuit current. It acts the opposite of a capacitor. Inductors: first turned on/off, acts like a break in the circuit - a long time later, it looks like a wire. (high resistance to low resistance). Capacitors: first turned on/off, looks like a wire. Later, it becomes a break in the circuit. 3. Inductance (L) - property of a particular inductor or coil. 4. emf induced in an inductor can be obtained by the definition of inductance. 5. Power consumed by an inductor can be found by . Not very useful...only gives power if current changes. 6. Energy stored by an inductor can be found by 7. RL Circuits - by Kirchhoff's voltage law, the differential equation . The solution is indicates that the time constant is . . Note that this