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lecture11_capacitors_energy_current_072611 - Physics 142...

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Unformatted text preview: Physics 142 7/26/2011 Dielectrics In In electrical systems, we want to store as large a charge separation as we can, but creating potential differences is expensive. We would like to find ways of reducing ∆V while keeping Q the same. In In biological systems, we often have charge separations, but the are almost always separated by spaces containing fluids – not by empty space. It It turns out that the answer to the first problem is provided by the second observation. Physics 142 Summer 2011 Consider what happens with an insulator We We know that charges separate + even with an insulator. + + This This reduces the field + inside the material, + just not to 0. + + The The field reduction factor is defined to be κ. 0 1 Einside material = Eif no material were there κ E –+ –+ –+ –+ – – – – – – – Physics 142 Summer 2011 Capacitors filled with an insulating material E= E= 1σ κ ε0 +– + +– + +– + +– Q κε 0 A d ∆V = Ed = κε A Q 0 εA C =κ 0 d +– – +– – +– – +– 0 Physics 142 Summer 2011 Dr. Nick Cummings 1 Physics 142 7/26/2011 Dielectrics If nonIf a non-conductor is put between the plates, there is still some polarization reducing the field so the voltage required for a given charge is reduced, i.e., C is increased. The The factor (assuming the space between the plates is filled) is called the dielectric constant, κ. C =κ ε0A d Physics 142 Summer 2011 What’s going on? When When we hook up a battery (or any other electric power source) and a bulb, the bulb glows but after a little start up time, stays at a constant brightness. We We want to understand what’s going on here. Physics 122 Electrical Current This This effect will involve large amounts of charge particles moving together. This motion of charges is called electrical current. Need Need to quantify the motion of charges Usually Usually we’ll be concerned with charges moving inside a material – Need to understand how that works Physics 122 Dr. Nick Cummings 2 Physics 142 7/26/2011 Moving Charges in a Neutral Conductor What What happens if we arrange charges to put an electric force on a neutral conductor? – Positive ions are fixed in a lattice – Some negative charges (shared electrons) are free to move Physics 122 Conductivity in a metal is complicated – and involves the quantum nature of electrons What What really happens is quantum mechanical – like covalent bonding. nuclei Shared electron cloud Physics 122 Conduction In In a crystal of a metal, all the atoms are bonded and some electrons shared. You You can think of some of the electrons as running in each direction along the chain. When an electric field is put on the chain, is shifts the balance and more electrons go one way than the other. Physics 122 Dr. Nick Cummings 3 Physics 142 7/26/2011 How to think about current? Unless Unless we are going to be materials science physicists, we don’t really need to understand the quantum view of conduction. Instead, Instead, we construct a bunch analogies that have some of the correct features. – water flow – air flow These These help us make sense of the fundamental laws that govern current flow. Physics 122 The fluid flow model Key Key concept: Pressure Recall: Recall: 1 2 3 4 – Pressure is like a tension but in 3D. – It pushes in all directions at once, so it has no direction. – Forces due to pressure occur when you only let it push on one side of an area. Then r r F = PA Physics 122 Viscous Drag A fluid flowing in a pipe doesn’t slip through the fluid pipe frictionlessly. The The fluid sticks to the walls moves faster at the middle of the pipe than at the edges. As a result, it has to “slide over itself” (shear). There There is friction between layers of fluid moving at different speeds that creates a viscous drag force, trying to reduce the sliding. The The drag is proportional to the speed and the length of pipe. Fdrag = 8πµLv Physics 122 Dr. Nick Cummings 4 Physics 142 7/26/2011 Implication: Pressure drop If If we have a fluid moving at a constant rate and there is drag, N2 tells us there must be another force to balance the drag. The The internal pressure in the fluid must drop in the direction of the flow to balance drag. Drag force Flow in Flow out Pressure force Pressure force Physics 122 upstream downstream Dr. Nick Cummings 5 ...
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