hy3: Gnral hyscs III 4/0/008 haptr Worksht lctrc Flds: onsdr a fxd pont charg of 0 µ (q ) q = 0 µ d = 0 a What s th agntud and drcton of th lctrc fld at a pont, a dstanc of 0? q = = 8x0 ˆ o d ˆ 6 N ( ) b A nd charg (q = -0 µ) s placd at pont What s th agntud and drcton of th lctrc forc xrtd on q 3? q q F = ( ) o d ˆ = -q = - 36 N ˆ {an attractv forc} Thr protons ar prsnt n th nuclus of a lthu ato, forng an qulatral trangl Th dstanc, r, btwn ach par of protons s 5 x 0-5 Lthu Nuclus r a What s th agntud of th lctrc fld vctor du to th lthu nuclus at pont, a dstanc of 5x0-0 fro th cntr of th nuclus? Snc d>>r: 3qp 0 N = 69x0 {radal outward fro nuclus} o d b What s th agntud and drcton of th total lctrc forc xrtd on an lctron postond at pont -8 F = q = = x0 N {nward towatd nuclus}
hy3: Gnral hyscs III 4/0/008 haptr Worksht 3 onsdr an lctrc dpol, q = 0 µ, sparatd by a dstanc (d) of 5x0-6 a Sktch th lctrc fld lns for th lctrc fld vctor du to th dpol b q r φ - What s th agntud and drcton of th lctrc fld vctor du to th dpol at pont, a dstanc (r) of 05 to th rght of th dpol? q = - = cos - sn j - cos - sn j o r or- ˆ ˆ q ( φ φ ˆ ˆ ) ( φ φ ) d - q ˆ -q ( ) ˆ -p ˆ - N sn φ j = j = j = - 36 0 ˆ 3 j or πεor d r ( ) or c What s th agntud and drcton of th lctrc fld du to th dpol at a dstanc of 05 drctly abov th dpol? p ˆ - N j = 7x0 ˆ 3 j πεo r r - -q 4 onsdr a unfor ln of charg wth a total charg of 5 p and a total lngth of 05 - a What s th agntud of th lnar charg dnsty? 5 p λ = = x0 05 - b Sktch th fld lns for th ln of charg n th dagra abov c Drv an quaton for th lctrc fld vctor at pont, locatd 03 abov th ln and cntrd btwn th nds Snc all but th vrtcal coponnt of cancls out: dq ˆ λdx y d ˆ y = d( cos φ ) = cos φ j = j o r o x y ( x y ) Solvng for :
hy3: Gnral hyscs III 4/0/008 haptr Worksht 3 = d = = o L yλ dx 3 o 0 x y λl ( ) y L y ( ) ˆj ˆj {n gnral, radally outward fro ln}
hy3: Gnral hyscs III 4/0/008 haptr Worksht 4 d What s th agntud of th lctrc fld vctor at pont? N = 044 {drctd away fro th ln of charg} Dtrn th lctrc forc vctor xrtd on an lctron placd at pont -0 F = q = = -70x0 N ˆj{nward toward th ln} f What s th acclraton of th lctron locatd at pont? F 0 a = = -77x0 ˆ j {nward toward th ln} s 5 onsdr a chargd rng, wth total charg of 4 and radus of 03 -q a What s th agntud of th surfac charg dnsty? 4x0 σ = = 85x0 π ( 03 ) -3-3 b Drv an quaton for th lctrc fld vctor at pont, locatd 5 to th rght of th cntr of th dsc Snc all but th radal coponnt of cancls out, stablsh dcosφ n trs of dq: dq ˆ σrdr x ˆ σxrdr d ˆ ( cos φ ) = cosφ= = 3 o d o x r ( x r ) o ( x r ) Solvng for : = d = R σx rdr ˆ 3 o 0 ( x r ) - σx ˆ σx = = - ˆ {away fro rng} 4 πε o o x ( x R ) ( x R ) R 0
hy3: Gnral hyscs III 4/0/008 haptr Worksht 5 d What s th agntud and drcton of th lctrc fld vctor at pont? -3 (85x0 )(5) = - ˆ 4 πε o (5) ((5) (03) ) 6 N = 5x0 ˆ {away fro rng} 5 Th plats of a paralll plat capactor hav a unfor charg of 0 and -0, rspctvly ach plat s a squar wth sds of lngth of 05 a What s th agntud of th surfac charg dnsty on ach plat? 0 σ = = 40 ( 05 ) b What s th agntud of th lctrc fld vctor nsd th plats of th capactor? Trat ach plat as a chargd flat dsc of nfnt R, x << R, thn th fld du to ach plat rspctvly s thn: σ ˆ plat = {both flds wll pont toward th rght} εo Th total lctrc fld btwn th plats s thrfor: σ ˆ N ˆ btwn plats = plat plat = = 45x0 εo c What s th lctrc forc xrtd on an lctron placd nsd th plats of th capactor? -8 F = q = = -7x0 N ˆj {to th lft} d What s th acclraton of th lctron whl t s n btwn th capactor plats? F a = = -79x0 ˆ j {to th lft} s For a 0 plat sparaton, calculat th fnal spd of an lctron (ntally at rst), that s placd at th ngatv chargd plat and just rachs th postv plat ˆ -0 ˆ v = v = - ad = - ( -79x0 )( ) s v = -8x0 ˆ {a bt unralstc h??}
hy3: Gnral hyscs III 4/0/008 haptr Worksht 6 Dpol Mont of Watr: 6 Watr s a polar olcul that conssts of H atos attachd to a cntral oxygn ato Th H atos ar orntd at an angl of approxatly 05 o ach of th H-O bonds has a dpol ont ( p ) assocatd wth t and togthr th dpol onts hav a rsultng nt dpol ont ( ) of 6x0-30 Th ffctv sparaton dstanc btwn th p HO rspctv postv (δ ) and ngatv (δ - ) chargs n ach O-H bond s 39x0 - a What s th agntud of th ffctv dpol ont of th ndvdual O-H bond for watr? o p ˆ HO = p p = qdcos(55 )j = ph O -0 p = p = p = = 5x0 o cos(55 ) b Dtrn th agntud of th charg (δ) for th ndvdual O-H dpol -30-8 p = qd = δd= 5x0 δ= 3x0 O O δ δ H δ θ=05 O c alculat th torqu on a watr olcul du to th lctrc fld of a chargd sphr (q sphr = -5x0-6 ) at a sparaton dstanc of 005, whr th drcton of th lctrc fld s orntd at an angl of 30 o to p qsphr = = 54x0 o r τ 6 N ( ) o -3 = p = psn30 = 7x0 N d What s th potntal nrgy of th watr olcul n ths lctrc fld? o -3 U = p = pcos30 = 9x0 J HO δ H