Knight_29_30_voltage_capacitors_lect - 29&30-1(SJP phys1120...

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29&30-1 (SJP, phys1120) Electric Potentials: We've been talking about electric forces, and the related quantity E = F /q, the E field, or "force per unit charge". In 1110, after talking about forces, we moved on to work and energy Quick Review of work and energy: The work done by a constant force, F, moving something through a displacement "d", is W = r F " r d = F || d = Fd cos # More formally, if F varies as you follow some path: W = r F " d r r # . E.g. if you (an "external force") lift a book (at constant speed) up a distance d, Newton II says F _net = m a , i.e. F _ext - F _g = 0 (because, remember, if speed is constant => a =0) or F _ext = mg. You do work W_ext = F_ext*d = +mgd (The + sign is because θ is 0 degrees, your force is UP, and so is the displacement vector) The gravity field does W_field = -F_g*d = -mgd (The minus sign is because θ is 180 degrees, the force of gravity points DOWN while the displacement vector is UP) The NET work (done by all forces) is W_ext+W_field = 0, that's just the work- energy principle , which says W_net = Δ KE (=0, here) You did work. Where did it go? NOT into KE: it got "stored up", it turned into potential energy (PE). In other words, F_ext did work, which went into increased gravitational potential energy. For gravity, we defined this potential energy to be PE = mgy, so ! PE = mg(y_final - y_initial) = + mgd (=W_ext) (The change in PE is all we ever cared about in real problems) Summary: If you do work on an object in a "conservative" force field: ! PE = W_"by you" = -W_"by the field"= " r F field # d r r $ Knight generally uses the symbol "U" for "Potential Energy", by the way. ! d F F _ext F _g = mg
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29&30-2 (SJP, phys1120) Now, let's drop the book, and see what happens. There is no more "external force" touching the book (like "me" in the previous example), only gravity acts. (Neglect friction) Energy conservation says PE i + KE i = PE f + KE f , i.e. mgd + 0 = 0 + 1 2 mv f 2 . This formula gives a quick and easy way to find v_f. The concept of energy, and energy conservation, is very useful! Another way of rewriting that equation is ( PE f ! PE i ) + ( KE f ! KE i ) = 0, i.e. " PE + " KE = 0, or " E tot = 0 If only conservative forces act, ! U (i.e. ! PE) is independent of the path taken. (End of quick review of work and energy!) There is an electric "analogue" of the above examples: Consider 2 charged parallel metal plates (called a "capacitor"), a fixed distance d apart. Between the plates, E is uniform (constant), and points from the “+” towards the “-“ plate. Imagine a charge +q, initially located near the bottom plate. The force on that charge is F_E =+q E (down, do you see why?). (Let's totally neglect gravity here!) Now LIFT "q" from the bottom to the top, at constant speed: You do work W_ext = r F ext " # d r r = F ext d =qEd The Electric field does W_field = r F E " # d r r = F E d cos(180) =qEd(-1) . (Do you understand those signs? Think about them!) Just like the previous case: you did work, but where did it go? As before, it didn't turn into KE, it turned into potential energy.
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Knight_29_30_voltage_capacitors_lect - 29&30-1(SJP phys1120...

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