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 h = 1 m A man lifts a 5 kg rock 1 meter off the ground. The potential energy of the rock is about A) (5 kg)  ( 1 m) = 5 J B) (5 kg)  g  1m  50 J C) 2(5 kg)  (1 m) = 100 J D) (5 kg)  g 2  500 J About how much work did he do? A) 5 J C) 50 J B) 100 J D) 500 J E) cannot be determined from the information given Gravitational potential energy = mgh

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 Which experiences the greater acceleration? (1) proton (2) electron (3) both have equal acceleration (4) neither will accelerate at all. A proton and an electron are each accelerated by moving the same distance across a region of constant electric field, E.

Electric Energy Which experiences the bigger increase in Kinetic Energy ? (1) proton (2) electron (3) both receive the same increase in KE increase in KE (4) neither --  KE = 0 for both A proton and an electron are each accelerated by moving the same distance across a region of constant electric field, E.

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  v 2. in separating unlike charge and/or building concentrations of like charge. Electric Potential Difference Work q voltage is related to the work done (by a generator or even chemically by a battery) V =

Work q  PE q Electric Potential Difference V = = Notice the amount of potential energy stored by any charge in a potential V is 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.

m  PE = work required to move an object against a “restoring” force (F avg )(x ) moved against that force g d Work = mgd depends on m, g, d

m g d Work = mgd depends on m, g, d E +q+q Work = Fd +q+q d = (qE)d(qE)d Work q =EdEd V = Ed depends on q, E, d

E +q+q +q+q d V = Ed Work = (qE)d For a uniform E-field But moving toward a tightly concentrated charge Q +q+q

But for a tightly concentrated charge Q +q+q V = EdWork = (qE)d Since the E-field keeps changing so fast! Instead : Work = k  k qQ R stop qQ R start

Q and the voltage of a concentration of charge Q build up across the surface of a spherical conductor of radius, R:

            

MIT’s Van de Graff Generator 1935 Robert Jamison Van de Graff

750 keV = 750,000 eV Fermi National Laboratory

1.5 MeV electron accelerator Basel, Switzerland

Two identical conducting spheres (with insulated handles) are charged to different voltages, V 1 >V 2. The two spheres must be a. charged with Q 1 >Q 2. b. charged identically with Q 1 = Q 2. c. charged with Q 1 <Q 2.

Two identical conducting spheres (with insulated handles) are charged to different voltages, V 1 >V 2. 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, V 1 >V 2. Having been touched together a. both spheres are now at V 1. b. both spheres are now at V 2. c. both spheres are now at a voltage in between V 1 and V 2.

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. = or

But check out a comparison of the charge DENSITY across the surface of each: If then And how do these compare: 1. > 2. = 3. <

But check out a comparison of the charge DENSITY across the surface of each: Although Q > q The charge density across the surface of the smaller sphere is HIGHER! Charge is crowded together much more tightly on the smaller sphere!

7. is zero QUESTION 1 As explained in slide 2! 7. is zero QUESTION 2 As argued in slides 4-5! (B) (5 kg)  g  1m  50 J QUESTION 3 Gravitational potential energy = mgh (C) 50 J QUESTION 4 Work done = change in energy it produces (2) electron QUESTION 5 q electron =q proton so since F=qE both proton and electron experience the same sized force! However, since m electron << m proton, they respond differently! The electron will move with an acceleration ~2000  greater than the proton (since the proton is almost 2000  heavier! both receive the same (3) both receive the same increase in KE increase in KE QUESTION 6 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!