Solution: (a) C 4 1 AI IC 4. (b) IBC 4
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1 C A C C R A C R C R C sin 9 sin. A cuent f is maintaine in a single cicula lp f cicumfeence C. A magnetic fiel f is iecte paallel t the plane f the lp. (a) Calculate the magnetic mment f the lp. (b) What is the magnitue f the tque exete by the magnetic fiel n the lp? (a) (b)
2 . A magnetize sewing neele has a magnetic mment f. At its lcatin, the Eath's magnetic fiel is nthwa at belw the hizntal. (a) entify the ientatin f the neele that epesent the minimum ptential enegy. (b) entify the ientatin f the neele that epesent the maximum ptential enegy f the neele fiel system. (c) Hw much wk must be ne n the system t mve the neele fm the minimum t the maximum ptential enegy ientatin? Hizn (a) Ptential enegy is minimum when it is paallel t the magnetic fiel. i.e. the sewing neele is pinting nthwa at belw the hizntal. U = cs = in the case. (b) Ptential enegy is maximum when it is antipaallel t the magnetic fiel. i.e. the sewing neele is pinting suthwa at abve the hizntal. U = cs = in the case. (c) W = PE = U max U min = ( ) =
3 3. A ectangula cil cnsists f N clsely wappe tuns an has imensins a an b. The cil is hinge alng the y axis, an its plane makes an angle θ with the x axis (see figue belw). (a) What is the magnitue f the tque exete n the cil by a unifm magnetic fiel iecte in the psitive x iectin when the cuent is in the iectin shwn? (b) f yu ae lking wnwa fm the psitive y iectin, what is the expecte iectin f tatin f the cil? (a) Tp view: y x z sin Nabsin Nabsin (9 Nabcs ) (b) y z x Using ight han ule, iectin f tque is given in the figue. f yu ae lking wnwa fm the psitive y iectin, the tques is in the y iectin (i.e. clckwise).
4 . The t in a cetain electic mt is a flat, ectangula cil with N tuns f wie an imensins a by b. The t tates in a unifm magnetic fiel f. When the plane f the t is pepenicula t the iectin f the magnetic fiel, the t caies a cuent f. n this ientatin, the magnetic mment f the t is iecte ppsite the magnetic fiel. The t then tuns thugh nehalf evlutin. This pcess is epeate t cause the t t tun steaily at an angula spee f. (a) Fin the maximum tque acting n the t. (b) Fin the peak pwe utput f the mt. (c) Detemine the amunt f wk pefme by the magnetic fiel n the t in evey full evlutin. () What is the aveage pwe f the mt? (a) sin is maximum when 9 an sin max Nab (b) sin iectin f is pepenicula t the pape plane. is als pepenicula t the pape plane. P Nab sin Nab sin t P is maximum when 9 P max Nab an sin (c) Amunt f wk ne by the magnetic fiel in evey eculutin Nab Nab () Pei T Aveage pwe T/ Nab sin t t [Nab cs t ] (Nab cs ) (Nab cs ) (Nab) Nab T/ (Nab)
5 5. A Halleffect pbe peates with a cuent. When the pbe is place in a unifm magnetic fiel f magnitue, it puces a Hall vltage f V H. (a) When it is use t measue an unknwn magnetic fiel, the Hall vltage is V H. What is the magnitue f the unknwn fiel? (b) The thickness f the pbe in the iectin f is t. Fin the ensity f the chage caies, each f which has chage f magnitue e). (a) Equatin f mtin : V FE F e ev VH v an VH ' vunknwn VH ' v ()/() V v H VH ' V H unknwn unknwn VH ' V H unknwn V () () v (b) V H V H v ut nev A nea v net nea n V et H
6 6. n an expeiment esigne t measue the Eath's magnetic fiel using the Hall effect, a cppe ba f thickness t is psitine alng an east west iectin. Assume numbe f electns pe cubic mete be n an the plane f the ba is tate t be pepenicula t the iectin f. f a cuent in the cnuct esults in a Hall vltage f V, what is the magnitue f the Eath's magnetic fiel at this lcatin? Eath s magnetic fiel Equatin f mtin : F E F V nea V e ut nev A ev v net V nea Vnet v
7 7. (a) n the figue belw fin the iectin f the cuent in the wie that wul puce a magnetic fiel iecte as shwn. Ans: (b) n the figue belw fin the iectin f the cuent in the wie that wul puce a magnetic fiel iecte as shwn. Ans: (c) n the figue belw fin the iectin f the cuent in the wie that wul puce a magnetic fiel iecte as shwn. Ans:
8 8. n Niels h's 93 mel f the hygen atm, an electn cicles the ptn at a istance f R with a spee f v. Cmpute the magnitue f the magnetic fiel this mtin puces at the lcatin f the ptn. v e R =? R e ut (T pei f T e ev R R v ev ev R R R R the cicula mtin f the electn)
9 9. Cnsie the fllwing figue. (a) A cnucting lp in the shape f a squae f ege length caies a cuent as in the figue abve. Calculate the magnitue an iectin f the magnetic fiel at the cente f the squae. (b) f this cnuct is eshape t fm a cicula lp an caies the same cuent, what is the value f the magnetic fiel at the cente? magnitue (a) A s ˆ We just nee t calculate the magnetic fiel ue t segment A an then multiply the esult with 8 f the sque. it Savat Law : s ˆ s sin A ut s tan s cs cs cs 9 sin sin (9 ) cs Substitute these esultes int () : ( )cs cs A ( ) cs ()
10 8 Magnetic fiel at cente ue t the whle squae ) ( ] [sin cs cs A A A / A / A A (b) f the cnuct is eshape t a cicula lp, cicumfeence = ) ( R R R
11 . A cuent path shape as shwn in the figue puces a magnetic fiel at P, the cente f the ac. f the ac subtens an angle f θ an the aius f the ac is R, what ae the magnitue an iectin f the fiel puce at P if the cuent is? Magnetic fiel ue t the tw staight cuents = (why?) Magnetic fiel ue t the ac R R Magnetic fiel at pint P R R
12 . Tw lng, paallel wies cay cuents f an in the iectins inicate in the figue belw, whee is the istance between the tw wies. Take the psitive x iectin t be t the ight. (a) Fin the magnitue an iectin f the magnetic fiel at a pint miway between the wies. (b) Fin the magnitue an iectin f the magnetic fiel at pint P, lcate abve the wie caying the cuent. (a) ) ( ) ( ) ( x y / /
13 (b) x axis. cunteclckwise fm the tan 8 Diectin ) ( Magnitue ] )xˆ [( )xˆ ( xˆ ) xˆ ( xˆ xˆ xˆ xˆ 5 cs xˆ 5 cs ut x y = 5 5
14 . The tw wies shwn in the figue belw ae sepaate by an cay cuents f in ppsite iectins. (a) Fin the magnitue an iectin f the net magnetic fiel at a pint miway between the wies. (b) Fin the magnitue an iectin f the net magnetic fiel at pint P, t the ight f the wie n the ight. (c) Fin the magnitue an iectin f the net magnetic fiel at pint P, t the left f the wie n the left. (a) ) ( ) ( ae pinting int the page. an bth As shwn in the figue,
15 (b) () (c) (3) ()
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