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What is the electric field at the very CENTER of this spherical conductor? ++ ++ ++ + ++ E = 0!! ++ + + + + + + + + + + ++ +++ ++ + + ++ ++ + + + + + + + + + + + + + + + + + + + + + + ++ ++ ++ ++ The electric field at this off-CENTER point within the spherical conductor +++ ++ + + ++ ++ + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ ++ ++ ++ Nearby charges create a strong electric field. ++ ++ ++ ++ + Much farther away, individual charges have a much smaller effect, but there are much more of them! ++ All of this balances beautifully and the electric field even at off-center points (in fact, EVERYWHERE) within the conductor is zero! That’s why fan motors or transformers (which can produce fluctuating electric fields) are often shielded from the more sensitive parts of circuits by “cans” of conducting metal. Conducting panels when screwed in place provide a surrounding shield against stray electric fields! Concept Review A man lifts a 5 kg rock 1 meter off the ground. The potential energy of the rock is about h=1m A) (5 kg)( 1 m) = 5 J B) (5 kg)g1m 50 J C) 2(5 kg)(1 m) =100 J D) (5 kg) g2 500 J Gravitational potential energy = mgh About how much work did he do? A) 5J C) 50 J B) 100 J D) 500 J E) cannot be determined from the information given Concept Review Test The balls in the figure are identical. When released from rest, which has a greater kinetic energy when it gets to the bottom of its ramp? A) B) C) both the same Electric Energy A proton and an electron are each accelerated by moving the same distance across a region of constant electric field, E. Which experiences the greater acceleration? (1) (2) (3) (4) proton electron both have equal acceleration neither will accelerate at all. Electric Energy A proton and an electron are each accelerated by moving the same distance across a region of constant electric field, E. Which experiences the bigger increase in Kinetic Energy? (1) proton (2) electron (3) both receive the same increase in KE (4) neither -- KE = 0 for both h Recall the work done in elevating a bag of fluids W = mgh results in added pressure P = gh in this I.V. tube: Just like • the work done mgh in lifting (pumping water) • creates added pressure P = gh • which can be exchanged as fluid kinetic energy = ½ v2. voltage is related to the work done (by a generator or even chemically by a battery) in separating unlike charge and/or building concentrations of like charge. Electric Potential Difference Work V= q Electric Potential Difference Work V= q PE = q Notice the amount of potential energy stored by any charge in a potential V is PE V q PE qV charge voltage = ENERGY --- + ++ -- + ++ -- + ++ Separating clinging fabrics is doing work (W = Fd) against the electric fields that try to hold them together. Prying your shoe from carpet involves a tiny bit more work than just lifting the weight of your foot. -+++++++++++++++++++++ + (Favg)(x against moved ) that force PE = work required to move an object against a “restoring” force g Work = mgd m depends on m, g, d d g Work = mgd m depends on m, g, d d E Work = Fd +q = (qE)d depends on q, E, d d +q Work = Ed q V = Ed E +q For a uniform E-field +q Work = (qE)d V = Ed d But moving toward a tightly concentrated charge +q Q But for a tightly concentrated charge Work = (qE)d V = Ed Since the E-field keeps changing so fast! Instead: qQ qQ Work = k -k Rstop Rstart +q Q and the voltage of a concentration of charge Q build up across the surface of a spherical conductor of radius, R: Q Q V k R -- - +++++++++++++++++++++ + +++++++++++ + +++ - -++ --+++ Robert Jamison Van de Graff MIT’s Van de Graff Generator 1935 Fermi National Laboratory 750 keV = 750,000 eV 1.5 MeV electron accelerator Basel, Switzerland Two identical conducting spheres (with insulated handles) are charged to different voltages, V1>V2. The two spheres must be a. charged with Q1>Q2. b. charged identically with Q1= Q2. c. charged with Q1<Q2. Two identical conducting spheres (with insulated handles) are charged to different voltages, V1>V2. When touched together a. charge flows from 1 2. b. all charge stays in place. c. charge flows from 2 1. Two identical conducting spheres (with insulated handles) are charged to different voltages, V1>V2. Having been touched together a. both spheres are now at V1. b. both spheres are now at V2. c. both spheres are now at a voltage in between V1 and V2. A large conducting sphere of radius R initially carries an initial charge. When touched to a smaller, uncharged conducting sphere of radius r < R charge flows to the smaller sphere until 1. each sphere carries half the total charge. 2. each sphere carries the same density of charge. 3. charge is divided between them in proportion to their radii: q/Q = r/R. Two conducting spheres (radius R and r), after touching, are at the same potential. Q q k =k R r r q Q R or q r Q R But check out a comparison of the charge DENSITY across the surface of each: Q 2 4R r q Q R q 2 4r q rQ / R If then 2 2 4r 4r Q 4rR And how do these compare: 1. > Q Q 2. = 2 4rR 4R 3. < But check out a comparison of the charge DENSITY across the surface of each: Q 2 4R Although Q >q q 2 4r Q 2 4R q 2 4r The charge density across the surface of the smaller sphere is HIGHER! Charge is crowded together much more tightly on the smaller sphere! QUESTION 1 7. is zero QUESTION 2 7. is zero As argued in slides 4-5! (B) (5 kg)g1m 50 J QUESTION 3 As explained in slide 2! Gravitational potential energy = mgh QUESTION 4 (C) 50 J Work done = change in energy it produces QUESTION 5 (2) electron qelectron=qproton so since F=qE both proton and electron experience the same sized force! However, since melectron<< mproton , they respond differently! The electron will move with an acceleration ~2000 greater than the proton (since the proton is almost 2000 heavier! QUESTION 6 (3) both receive the same increase in KE Both experience the same F=qE and travel the same distance d under its influence. So the same amount of work W=Fd is done on each. QUESTION 7 We’ll discuss this one on Wednesday!