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the_e_field_coulomb_gravitational

# the_e_field_coulomb_gravitational - THE E—...

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Unformatted text preview: THE E— FIELD (COULOMB)/GRAVITATIONAL FIELD FORCE BETWEEN TWO POINT CHARGES FORCE BETWEEN TWO POINT MAS SES GM M FE: k6 QIQZ A FG : _ 12 2 7;} —> 7‘2 a r N— m2 G: 6. 7x10—11 N — 2 2 k3 = 9x109 Cam (kg) Q1, Q2 same Sign FE ||+r REPULSIVE (80TH FORCES QWWM’?) fig/V Q1 FE /Q2 Q1, Q2 have opposite signs. ‘ ,- FE n- I? ( ,30 T H Roma; JIM/94%») ATTRACTIVE 492T Q7 r3 6 FG ALWAYS ATTRACTIVE FGll—f (BOTH Fahd/Es LNW ) NOTICE THAT THE FORCES OCCUR AS ACTION- REACTION PAIRS IN EVERY CASE. __) |F12= 4:21] Thve E’dguﬂT/QNS ﬂEPIQEfEﬂ/T 7W0 .r-a/QCES Many Point Charges Force on Q 2 QQ- E : ke - - 2 rz'j Note: Right side involves addition of vectors. —> J 7’3 l 717' SPECIAL CASES 1. Q at x=0, Q2 at x=L. Where to locate Q3 so F3 force on Q3 is zero. ._) Q3 must be’on the line joining Q1 and Q2. L x 2 Q 1 _2_ + 91 0 x ‘ L 0—. Q1 Q3 Q2 2. Q at x=0, —|Q2| at x=L. F3 will be zero if L x = \@ when Q1) iQ2| Q2 3. Q at x=-a, Q at x= +a. What is force on C] at (O, y) 2k Qy F, = ‘3 “ :(y) (y2 + a2)%y What if we have — lql at (0’)”) ~2kquyJ‘) (y2 + a2>% who»! ,0 Let: W} m CRJQ‘Q ‘(f’ << CL» (‘1’; ‘v~~m- —- 5* err-*- In this case, force is proportional to displacement y and opposite to it so — lql will show Linear ﬂ .__, WE Harmonic oscillations. QUESTION: Why is there a force between two charges(rnasses) when they are far apart from one another. To answer this we develop the concept of a FIELD COULOMB E- FIELD GRAVITATIONAL(GF) FIELD _’ —> If there is amass M sitting at x=0, the space around it is not empty. M creates a gravitational (G1,) ﬁeld which ._) permeates all of space. If you place a test charge q in permeates all of space. If you place a test mass m in the this E ﬁeld, it experiences a force FE : q E g ﬁeld It experrences a force —> _) —> FG : mGF —> —> If there is a charge Q sitting at x=0, the space around it is M empty. Q creates a coulomb E ﬁeld which —) 1. Single +ive charge Q at r=0. ’29 E227” % r _ l 669% Acts like a “source” of an E ﬁeld which points radially G _ _ GM f a 1? “ 2 outward a 7” 2, single 4V6 charge at PO. ALWAYS INWARD RADIALLY. E = — kc g? —> r Acts like a “sink” of E ﬁeld which pts. Radically inward. 3. E ﬁeld ofDipole: —'Ql at x=~a +Qatx=a k 2aQ , ti” = 0, E :——“ x a 1 ( y) 401) (y2+a2)3/2 at P2 =(x,0) E(x):— 1:64an (x2 —a2)2 Next, deﬁne dipole moment p = ZaQJE -ke 19 53(3)) = y3 —> 2kg}? E = a \$05) x3 When x,y >>a that is far away from dipole ...
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the_e_field_coulomb_gravitational - THE E—...

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