RQ20.3!"!"=+#$()!"%"×!"&"!"%"'#$!"&"" ()*" (+ " ,-.$For the force to be inward (to turn the positively charged nucleus into a circular orbit), the magnetic field must beout of the page. For the magnitude, with r = radius of orbit and T = period (time for one revolution):!"##= $ = #%"&/01 23°()= #%"& (nonrelativistic approximation)&=!"#%#=!#π#' #%#=π!%'=π4 ×53−67.89(:$;×53#61)<:$089(:$ 5=; × 53−52>()?3 × 53−2/()=5=; " *$/:-RQ20.9θωI outI inBBFmagFmagFusFush θωθωθθ/01/01##/01#$9+/@0.A*"B0@$"-1C:$+*"01""/01&()&)("&)"&*====At the instant shown in the diagram, the magnetic force on a positive carrier in the right-hand wire is out of thepage, so conventional current I comes out of the page.We have to apply forces (Fus on the diagram) to oppose the ""D!"+,×!"&, magnetic forces on the current-carrying wires.We twist the loop counter-clockwise against the clockwise twist due to the magnetic forces.RQ20.10""#"&"#%01/):-*01."@-0:/:$1.*A"E-----+++++!"F mag=−e()!"v ×!"B "" !"F elec=−e()!"E C!"E C!"E CMagnetic force ""−%()!"",×!"&, on an electron inside the rod polarizes the rod as shown.A Coulomb electric field ""!"*,- appears inside the rod as shown, due to the surface charges.Polarization proceeds until $%.%/0#1/= $!234%01/:%*-=%"& /01 23°()⇒*-="& ""!"*,- is uniform throughout the rod, since !"", and ""!"& are the same everywhere. The surface charges will arrangethemselves to make a uniform electric field. ""∆5≡−!"*,-•6l∫=*-+="&+, since ""!"E C is uniform.∆5 = %!7 − #01*%#42.D = %!7 , since I = 0, so emf = ECL = vBL.Or, ""$9+ =!"$,8-•6l9∫=%"&+%= "&+ = *-+.Once the rod is polarized, I = 0, so there is no ILB magnetic force opposing the motion. So no force is required tokeep the rod moving at a constant speed v on the frictionless
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