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Name: k~Je. Vnid: _ _ _ _ _ _ _ _ _ _ _ __ 1 Final Exam Discussion TA: _ _ _ _ _ _ _ _ __ y Show all work!! Report all numbers to three (3) significant figures. A. Find an exact for the electric field E at a point P located at (x,y)=(O,a) from a dipole consisting of a positive charge (+q) and negative charge (-q) at positions (-a,0) and (+a,0) as shown. Vse the symbols ~(Coulomb constant), and unit E-;: t J'-) t t ~ j vectors t and j, as needed. VectorE= _ _ _ _ _ __ -\-.!:h(J>~t;O ZJ:\i.- LEx == !:1L 2£A'2. LEi;;:: ~ &\\1\'\\0 - ~~l. )\V'\l\~o C1»l.\\- ~ E= *,-~--=~T ~ -- B. !:&; Cb> ,-\-t;" :: () = Q t-L\ =- t 1 ----~--.-~~~-~-- A cloud of positive charge has a volume charge density of P = Po rlR where r is the distance from the center of a sphere of radius R and Po is a constant. Find the magnitude of the electric field E at a point inside the sphere at distance r < R. Ii'J ::::'f:l t\V\ ~ l\ ~M ~. ~ C. ·9 e \' Two protons are held at rest at a separation d = 2.2 x 10 m = 2.2 nm. If they are released and fly apart to large (infinite) distance as a result of electric repulsion. what is the final speed v of each proton? v= _ _ _ _ _ _ _ __ =E~\j> H +e +e .11(----4.'--....""'--""'--.. . d Ph~sics 2220 Spring 2013 Name: All / G-b 6 -c./ Unid: _ _ _ _ _ _ _ _ _ _ _ __ Discussion TA: Bt'n 2 Final Exam --------------- Broml('~ Show all work!! Report all numbers to three (3) significant figures. A. The strengtlrofthe magnetic flux through a curved open surface So (the "net" 2 part of the "butterfly net" shown) is $B B = 1.45 T·m. The radius of the net's hoop is r 0.24 m and the magnetic field B in the plane of the hoop is uniform and perpendicular to the plane ofthe hoop, as shown. Find the magnitude ofB. B= <3.0( T --------------- For "'- c.loS1>oI s().,f,,(~ Iik-d')uY' nd Cfn c{ flo; f Flu x t' (\ Ff() x C) cA- So cfs ~:::: 1::6 ::: B., A ~ J net hoop S/I'\ce &t/l or (S f~rp-t'1 .'cvltfr to It ihen CPs =8,4 a'lJ &= Ji--=-~L - 23.0/T I'S B. A very long hollow PiP~as inner [Jlihs a and outer radius b. A uniform current density J J flows vertically upward between the inner and outer radii as shown. Find B, the magnitude of the magn~e~tt~~1i)ce r> b from the pipe's axis. B(r) = U C, /1'1 ~ k V -" f/I (Y\ J g.J-f, ~7 c. pM ~ ':, t.. II W VII(. J-,... Ve ~ }{oIenc -t- ~/tfNen{.'''( c<#)m",t -Vl~(e B2f rr- :::){o "Ie1l6 -=- )JO J AHI!(ur.n.t -'AoJ(J7b2,..T1~~ 13 2/1 (' ~ flo J n ~~~ B'" .Jja:Jlh7..« 2) 2Y' A square wire loop of length L to a side rotates on a central axis that is perpendicular to a magnetic field of strength 0.1 T. If the loop is rotating at an angular frequency of ro = 60 rad/s, what is the maximum EMF emax in the As.>(/ loop? 8max= (YJ.(!. 6V U~e ~r",d qy~ JqW' ~B:::- L ==.11'1 _/ -7 . B# A =lgllA Icase B axis I\nOWff =-cl'lf.::: -W/tB <;,hWt) ",~e" '7i~ (.u ~ )n=' /0(' -/ ', whE ·1-:::: {J.) L2-'6= (, V \. R... wt ---; ~4 · M~A fov- t)[/r C~t;.{ I5A{c?5 wt). We. tl'lf"'WA 'S j L--Mf '