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test 3 - PHYS 1 12 Test 1 Summer 2009...

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Unformatted text preview: PHYS 1 12 - Test 1 ' Summer 2009 ——————_—___________ Problems: In order to qualify for pom‘al credit you have to provide at least a logical start towards a solution, even r'fr't may beflawed. Do not flood the space with obviously useless information. -———————_—.—_.__________ P1: A charge Q= —3.4 uC is placed at a distance )1 = 0.1 l in above a very long straight line of charge with uniform linear charge density It = —5.5 pC/m as in the figure. A test point charge :1 = 1-049 uC is “I" placed in point A where it floats in static equilibrium at height hfZ T above the line of charge. a) [3] Sketch a cylindrical Gaussian of arbitrary radius r and length - L, coaxial with the line of charge. Write out an expression for the E t h electric flux through its surface in terms of the field E 4, r and L. a ' Recall that the area of the q if, fl curved surface of a cylinder A i \(f/ \H 18 Its Circumference times it . _ len . , ‘13:; -Eh'3\1trl:_ gm El K J éh - L. i I, b) 15] Use part (a) and Gauss’s Law to derive a symbolical $25 1 expression for the magnitude E; of the electric field produced by the line at distance r from it, in term of .2, so, and r. E; E (l, in r L ’ Lh: Q in @th E 1‘— it'b E 3’" :7‘ I” e) [4] Use vector arrows to represent the electric field vectors EQ and EA created by the charge Q and the line of charge it in point A. Then calculate the magnitude of each of the two fields in point A. l Kai 4343:; 'l«OllX|0'3 EL 2 gig T5: ; Its-1,205? X ’l EA=L: _$_3J(:U"C— ': — N m -—»= to WW 4/ d) [4] Calculate the net electric field in point A. . x (Weir—75 a -\,01 AWE ,2 e} [4] Use the equilibrium between the electric and gravitational forces to calculate the mass m of the test charge q. l‘ @ if 7 ””56 , __ @ this :Wa 13E”, (’ifilélxlficmfi) : [2 WV" 3’ J ‘s—F 505 lit} '17. - ' s3. ...
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