MT 1 Physics

# MT 1 Physics - Probiem 2[25 A non-conducting sphere has...

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Unformatted text preview: Probiem 2 [25]. A non-conducting sphere has radius R and volume charge density pis centered at the origin. a) {5] What is the E—ﬁeld outside the. Sphere? Shoueur work. 7) i a t L‘TTR _ Gauss 5 i In; #3 f E 0m - Gm“ Eb E Gina") 19:3 b} [ID] A particle with charge. Q and mass m. is released from a point (I meters away from the surface of the sphere. Find the article’s s eed when it reaches a position 2d from the surface of the sghere. an \$33 +I>E;, =KE;*PEF I L— i 9.: .+ F. P 0 KG :0. S .— Rsrd 3' R+ 2‘1 c} 1'10] A uniform line charge with total charge Q _ _ d is oriemed radially with respect to the sphere with its ends :1! R and R+a'. What is the force on the line charge? I Hint: lzdrz—l r r 3. I'Scl'orc the dielectric is InscrrctL we have E93 0 Qd d C Q=cv,c= After the dielectric is inserted, the capacitor can be considered as two half—plales. one without the diclccu-ic, the other with lhc dielectric. Each half-plate forms a new capacitor‘ and die Iwo capacitors are in parallel because they have the same potential. Thu: half—plate. wilhoul the dielcciric has capacitance {:9 A / 2 so A C]_ _ I ('1 2d while lhc half-plalc with the diclctric (x = 7] has capacitance (Ken) AJ’Z 69A C3-—= , d d The equivalent capacitance is then 3 l: D A 2 d C' 281*82: Finally, we note mat the metal charge Q is unchanged before and aﬁer we inscn the dielectric because the capacuor has alvcddy bccn disconnected from lllc ballciy. Thcrcforc the new potential is V‘: Q /3€uA 2ch 2V c' 2d —3EDA 3 ' In other words. the potential has dropped lo two—lhirds of its original value. Problem 4 [10]. Two large copper plates are a distance it apart and have a uniform electric field between them. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and ﬁnd their distance from the positive plate when they pass each other. Use symbols for the various charges, masses, etc. ASKSJN \Jﬁlﬁ/M LLpCVﬁg [AM (QNGMh+ 1; IR HNL dIWCNM P{V‘O{hdg-(ch. 1:. +1.» plq'kS. (This will cancel out 6F ow' Rant answer.) TN queme 09H“. thn IK‘er, P{.V’d{hdi.cul1h- dxndhh :3 Hit“ Q .. 2.5 1° - Mf- WLU’L e. is H. chm-claw); claw-3,, owl MP *3 Ha from: Mr 1‘“ "bl “u. rmh)“ has (ﬁlmy-11 at _ 1 LE 1 Yr ' A(Mr Mu“ . (FA-{quad u cylafjl 4 Elana ' 2') t2 2 ﬁg) TL]. dds—no. 190M l—LL pox: w Us KP ail- Hﬁx NM,‘ x,= :(f) J8 - izsélﬁﬁfJ/SH Wt“; We" 5 and E has tang/(d 0.1- ou p/Dmutd :§ : 1:ng — )Pw E-‘o ‘v WWW (Pﬁﬂﬁdw QLOJ‘ (by Flt-N. :1 £120 (bth *3me a (kids. iglg‘m ) ...
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## This note was uploaded on 03/08/2011 for the course PHYS 8B taught by Professor Catherinebordel during the Spring '10 term at Berkeley.

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MT 1 Physics - Probiem 2[25 A non-conducting sphere has...

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