ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.

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1 GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: ALL QUSTIONS AR WORTH POINTS. WORK OUT FIV PROBLMS. NOT: Clealy wte out solutons and answes (ccle the answes) by secton fo each pat (a., b., c., etc.) Chapte m m F = G. Impotant Fomulas: Newton s Law of Gavtaton. F = k 4 πε = Coulomb s Law 3. F = = k, ε =8.85x - C /Nm, k=8.99x 9 Nm /C 4 πε 4. C=(A)(s) 5. d = lectcal Cuent dt 6. Chapte F = lectc feld, s a postve test chage; F s electostatc foce that acts on the test t chage 7. F =, lectostatc foce that acts on the patcle wth chage. = = k, lectc feld due to Pont chage 8. 4 πε = d = p, lectc feld on axs z due to an electc dpole πε z πε z p=d s an electc dpole moment wth decton fom negatve to postve ends of a dpole.

2 . = 4 πε z ( z + R ) 3/, lectc feld due to chaged ng. = 4 π ε z, lectc feld due to chaged ng at lage dstance (z>>r) σ z =, lectc feld due to chaged dsk ε z + R σ =, lectc feld due to nfnte sheet ε 5. τ = p = psn( θ ), Toue on a dpole n electc feld 6. U = p = p C o s ( θ ), Potental enegy of a dpole n electc feld. Chapte 3 7. Φ = Δ A, electc flux though a suface 8. Φ = d A, lectc flux though a Gaussan suface. 9. ε Φ = enc, Gauss Law ε d A =. enc, Gauss Law.. 3. σ =, Conductng suface ε λ =, Lne of chage π ε σ =, lectc feld between two conductng plates ε 4. =, Sphecal shell feld at R 4 πε =, Sphecal shell feld at <R

3 . = 3 4 πε R, Unfom sphecal chage dstbuton at R. =, Unfom sphecal chage dstbuton at >R 4 πε Chapte 4 3. Δ U = U f U = W, Change n electc potental enegy due to wok done by electostatc foce. 4. U = W, Potental enegy; W s wok done by electostatc foce dung patcle move fom nfnty. 5. V U W = =, lectc potental U U Δ U W f Δ V = V f V = = =, lectc potental dffeence f V = d s, Potental at any pont f n the electc feld elatve to the zeo potental at pont V V V = 4 πε, Potental due to pont chage. n n V 4 π ε = =, Potental due to goup of n pont chages. = d V = 4 πε d, Potental due to contnuous chage dstbuton.. V = ( ) / λ L + L + d ln, Potental due to lne of chage 4 π ε d. V σ ( z ) R z = +, Potental due to chaged dsk ε 3

4 pcos( θ ). V =, Potental due to electc dpole. 4 πε. = ˆ+ ˆj + kˆ, Calculatng electc feld fom the potental x x y z V =, y x V =, z y V = z ΔV =, Calculatng electc feld fom the potental n a smple case of unfom Δ s electc feld. U 3 3 = + +, Potental enegy of system of thee 4πε 4πε 3 4πε 3 chages. n j U =, Potental enegy of system of n chages 4πε =, j < j n U = Vothe () = n Vothe () = 4πε j j= j j j Altenatve expesson fo Potental enegy of system of n chages 4

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8 4. 9.6x^ 6 N 8

9 5. A unfom electc feld of 3N/C makes an angle of 5 wth the dpole moment of an electc dpole. If the toue exeted by the feld has a magntude of.5x -7 N m, what must be the dpole moment? F F + τ = p n scala fom τ = p snθ N m sn θ (3 N / C)sn 5 7 τ (.5 ) 9 = = =. C p C m x axs 9

10 6. Postve chage Q s dstbuted unfomly thoughout an nsulatng sphee of adus R, centeed at the ogn. A patcle wth postve chage Q s placed at x = R on the x axs. What s the magntude of the electc feld at x = R/ on the x axs? P S x R At x= R / chaged nsulatng sphee geneates electc feld Q R Q S = = dected to the postve decton of x axs 3 4 πε o R 8 πε o R A patcle wth a postve chage Q placed at a dtance 3 R/ fom x= R/ geneates electc feld dected to the negatve decton of x axs wth a magntude Q Q p = = 3R 9πε or 4πε o The esultant electc feld at x= R / s dected to the postve decton of x axs Q Q Q d has magntude of = = 8πε R 9πε R 7πε R an o o o

11 7. Two conductng sphees ae fa apat. The smalle sphee caes a total chage Q. The lage sphee has a adus that s twce that of the smalle and s neutal. Afte the two sphees ae connected by a conductng we, what ae the chages on the smalle and lage sphees? a) Afte connectng two sphees by a conductng we some some chage fom sphee wll be tansfeed to sphee. Ths tansfe wll poceed untll potentals of sphee wll be eual to potental. Ths tanslates nto Q Q Q = Q = () 4πε R 4πε R o o b) Of couse total chage should be conseved Q + Q = Q () c) Substtutng () nto () gves Q = Q ; 3 Q Q = 3 3Q = Q

12 8. What s the magntude of the electc feld at the pont (3.ˆ. ˆj+ 4. kˆ ) mf the electc potental s gven by V=.xyz, whee V s n volts and x, y, and z ae n metes? We apply x y z V = =.yz x V = =. xz y V = = 4.xyz z whch, at (x, y, z) = (3. m,. m, 4. m), gves ( x, y, z ) = (64. V/m, 96. V/m, 96. V/m). The magntude of the feld s theefoe = + + = 5V m = 5 N C. x y z