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3 PHYS 1202W MULTIPL CHOIC QUSTIONS QUIZ #1 Answer the followng multple choce questons on the bubble sheet. Choose the best answer, 5 pts each. MC1 An uncharged metal sphere wll (A) be repelled by a charged metal surface. (B) feel no force when brought close to a charged metal surface. (C) be attracted by a charged metal surface. (D) not enough nformaton MC2 Two dentcal conductng spheres A and B carry equal charge. They are separated by a dstance much larger than ther dameters. A thrd dentcal conductng sphere C s uncharged. Sphere C s frst touched to A, then to B, and fnally removed. As a result, the electrostatc force between A and B, whch was orgnally F, becomes: (A) F/2 (B) F/4 (C) 3F/8 (D) F/16 MC3 For a gaussan surface through whch the net flux s zero, the followng four statements could be true. Whch statement must be true? (A) No charges are nsde the surface. (B) The net charge nsde the surface s zero. (C) The electrc feld s the same everywhere on the surface. (D) No electrc feld lnes leave the surface. () There s precsely one dpole enclosed by the surface. MC4 A sold conductng sphere of radus ra s placed concentrcally nsde a conductng sphercal shell of nner radus r b1 and outer radus r b2. The nner sphere carres a charge Q whle the outer sphere does not have any net charge. The electrc feld for r b1 <r<r b2 s (A) (B) (C) (D) MC5 Two large parallel plates carry postve charge of equal magntude that s dstrbuted unformly over ther nner surfaces. Rank the ponts 1 through 5 accordng to the magntude of the electrc feld at the ponts, least to greatest. (A) 1, 2, 3, 4, 5 (B) 5, 4, 3, 2, 1 (C) 1, 4, and 5 te, then 2 and 3 te (D) 2 and 3 te, then 1 and 4 te, then 5 () 2 and 3 te, then 1, 4, and 5 te Physcs 1202W.200 February 6, :20 PM 1:10 PM

4 PHYS 1202W MULTIPL CHOIC QUSTIONS QUIZ #1 Answer the followng multple choce questons on the bubble sheet. Choose the best answer, 5 pts each. MC1 An uncharged metal sphere wll (A) be repelled by a charged metal surface. (B) feel no force when brought close to a charged metal surface. (C) be attracted by a charged metal surface. (D) not enough nformaton MC2 Two dentcal conductng spheres A and B carry equal charge. They are separated by a dstance much larger than ther dameters. A thrd dentcal conductng sphere C s uncharged. Sphere C s frst touched to A, then to B, and fnally removed. As a result, the electrostatc force between A and B, whch was orgnally F, becomes: (A) F/2 (B) F/4 (C) 3F/8 (D) F/16 MC3 For a gaussan surface through whch the net flux s zero, the followng four statements could be true. Whch statement must be true? (A) No charges are nsde the surface. (B) The net charge nsde the surface s zero. (C) The electrc feld s the same everywhere on the surface. (D) No electrc feld lnes leave the surface. () There s precsely one dpole enclosed by the surface. MC4 A sold conductng sphere of radus ra s placed concentrcally nsde a conductng sphercal shell of nner radus r b1 and outer radus r b2. The nner sphere carres a charge Q whle the outer sphere does not have any net charge. The electrc feld for r b1 <r<r b2 s (A) (B) (C) (D) MC5 Two large parallel plates carry postve charge of equal magntude that s dstrbuted unformly over ther nner surfaces. Rank the ponts 1 through 5 accordng to the magntude of the electrc feld at the ponts, least to greatest. (A) 1, 2, 3, 4, 5 (B) 5, 4, 3, 2, 1 (C) 1, 4, and 5 te, then 2 and 3 te (D) 2 and 3 te, then 1 and 4 te, then 5 () 2 and 3 te, then 1, 4, and 5 te Physcs 1202W.200 February 6, :20 PM 1:10 PM

5 The lectrc Feld (b) The feld strength at the pont z = R/ 2 s ( ) Q ( R/ 2) 2 Q = = ( R/ 2) + R z max 2 2 3/ R Model: Assume that the semcrcular rod s thn and that the charge les along the semcrcle of radus R. Vsualze: The orgn of the coordnate system s at the center of the crcle. Dvde the rod nto many small segments of charge q and arc length s. Segment creates a small electrc feld at the orgn. The lne from the orgn to segment makes an angle θ wth the x-axs. Solve: Because every segment at an angle θ above the axs s matched by segment j at angle θ below the axs, the y-components of the electrc felds wll cancel when the feld s summed over all segments. Ths leads to a net feld pontng to the rght wth = ( ) = cosθ = 0N/C x x y Note that angle θ depends on the locaton of segment. Now all segments are at the same dstance r = R from the orgn, so q q = = r πε0r The lnear charge densty on the rod s λ = Q/L, where L s the rod s length. Ths allows us to relate charge q to the arc length s through q= λ s= ( Q/ L) s Thus, the net feld at the orgn s ( QL / ) s Q = cosθ = cosθ s x 2 2 0R 0LR The sum s over all the segments on the rm of a semcrcle, so t wll be easer to use polar coordnates and ntegrate over θ rather than do a two-dmensonal ntegral n x and y. We note that the arc length s s related to the small angle θ by s= R θ, so x Q = cosθ θ LR 0 Wth θ dθ, the sum becomes an ntegral over all angles formng the rod. θ vares from θ = π/2 to θ =+ π/2. So we fnally arrve at x = Q Q 2Q LR = LR = LR π /2 π /2 Ñ cosθdθ snθ π /2 π / Copyrght 2013 Pearson ducaton, Inc. All rghts reserved. Ths materal s protected under all copyrght laws as they currently exst. No porton of ths materal may be reproduced, n any form or by any means, wthout permsson n wrtng from the publsher.

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