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Magnetic field

1Determine the initial direction of the deflection of charged particles as they enter themagnetic fields as shown in Figure

2,Consider an electron near the Earths equator. In which direction does it tend to deflect if itsvelocity is directed (a downward! (" northward! (c westward! or (d southeastward#

$!% proton travels with a speed of $.&& ' 1&m)s at an angle of $*.&+ with the direction of amagnetic field of &.$&& , in the -y direction. hat are (a the magnitude of the magnetic forceon the proton and (" its acceleration#

4,%n electron is accelerated through / 0&& from rest and then enters a uniform 1.*&2,magnetic field. hat are (a the ma'imum and (" the minimum values of the magnetic force

this charge can e'perience#

3!% wire /.4& m in length carries a current of 3.&& % in a region where a uniform magnetic fieldhas a magnitude of &.$5& ,. Calculate the magnitude of the magnetic force on the wireassuming the angle "etween the magnetic field and the current is (a &.&+! (" 5&.&+! (c 1/&+.

6.A nonuniform magnetic field exerts a net force on a magnetic dipole. % strong magnet isplaced under a hori6ontal conducting ring of radius r that carries currentIas shown in Figure. Ifthe magnetic field 7 ma8es an angle with the vertical at the rings location! what are themagnitude and direction of the resultant force on the ring#

7.% small "ar magnet is suspended in a uniform &./3&2, magnetic field. ,he ma'imum torquee'perienced "y the "ar magnet is 0.& 91&2$:m. Calculate the magnetic moment of the "ar

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magnet.

8. % long piece of wire with a mass of &.1&& 8g and a total length of 0.&& m is used to ma8e asquare coil with a side of &.1&& m. ,he coil is hinged along a hori6ontal side! carries a $.0&2%current! and is placed in a vertical magnetic field with a magnitude of &.&1& & ,. (a Determinethe angle that the plane of the coil ma8es with the vertical when the coil is in equili"rium. ("Find the torque acting on the coil due to the magnetic force at equili"rium.

5. % wire is formed into a circle having a diameter of 1&.& cm and placed in a uniform magneticfield of $.&& m,. ,he wire carries a current of 3.&& %. Find (a the ma'imum torque on the wireand (" the range of potential energies of the wire;field system for different orientations of thecircle.

1&. &./&& mm is used in a ?all2effect measurementof a uniform magnetic field perpendicular to the ri""on! as shown in Figure. ,he ?all coefficient

for silver is R? > &.40&91&21&m$)C. (a hat is the density of charge carriers in silver# (" If a current I> /&.& %produces a ?all voltage @V? >13.&A! what is the magnitude of the applied magnetic field#

1/. % &./&&28g metal rod carrying a current of 1&.& % glides on two hori6ontal rails &.3&& m

apart. hat vertical magnetic field is required to 8eep the rod moving at a constant speed ifthe coefficient of 8inetic friction "etween the rod and rails is &.1&

13. % wire having a linear mass density of 1.&& g)cm is placed on a hori6ontal surface that hasacoefficient of 8inetic friction of &./&&. ,he wire carries a current of 1.3& % toward the east andslides hori6ontally to the north. hat are the magnitude and direction of the smallest magneticfield that ena"les the wire to move in this fashion#

14. % lightning "olt may carry a current of 1.&& 9 1&0% for a short period of time. hat is theresulting magnetic field 1&& m from the "olt# Buppose that the "olt e'tends far a"ove and"elow the point of o"servation.

15. % very long straight wire carries current I. In the middle of the wire a right2angle "end ismade. ,he "end forms an arc of a circle of radius r! as shown in Figure. Determine themagnetic field at the center of the arc.

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16.,wo long! parallel wires are attracted to each other "y a force per unit length of $/& :)mwhen they are separated "y a vertical distance of &.3&& m. ,he current in the upper wire is/&.& % to the right. Determine the location of the line in the plane of the two wires along whichthe total magnetic field is 6ero.

17.,he magnetic coils of a to8ama8 fusion reactor are in the shape of a toroid having an innerradius of &.*&& m and an outer radius of 1.$& m. ,he toroid has 5&& turns of largediameterwire! each of which carries a current of 10.& 8%. Find the magnitude of the magnetic field insidethe toroid along (a the inner radius and (" the outer radius.

14. % single2turn square loop of wire! /.&& cm on each edge! carries a cloc8wise current of&./&& %. ,he loop is inside a solenoid! with the plane of the loop perpendicular to the magneticfield of the solenoid. ,he solenoid has $& turns)cm and carries a cloc8wise current of 13.& %.Find the force on each side of the loop and the torque acting on the loop.

19. Consider the hemispherical closed surface in Figure. ,he hemisphere is in a uniformmagnetic field that ma8es an angle with the vertical. Calculate the magnetic flu' through (athe flat surface B1 and (" thehemispherical surface B/.

20. % &./&&2% current is charging a capacitor that has circular plates 1&.& cm in radius. If theplate separation is0.&& mm! (a what is the time rate of increase of electric field "etween theplates# (" hat is the magnetic field "etween the plates 3.&& cm from the center#

21. Calculate the magnetic field strength H of a magneti6ed su"stance in which themagneti6ation is &.44& 9 1&%)m and the magnetic field has magnitude 0.0& ,.

22. A very lng, t!in "tri# f $etal f %idt! w carrie" a c&rrentI alng it" lengt! a" "!%n in 'ig&re (30.49. 'ind t!e$agnetic field at t!e #intP in t!e diagra$. )!e #intP i" in t!e #lane f t!e "tri# at di"tance b a%ay fr$ it.

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/$.,wo identical! flat! circular coils of wire each have 1&& turns and a radius of &.3&& m. ,hecoils are arrangedas a set of ?elmholt6 coils (see! parallel and with separation &.3&& m. Eachcoil carries a current of 1&.& %. Determine the magnitude of the magnetic field at a point onthe common a'is of the coils and halfway "etween them.

24.,wo circular loops are parallel! coa'ial! and almost in contact! 1.&& mm apart (Fig.. Eachloop is 1&.& cm in radius. ,he top loop carries a cloc8wise current of 10& %. ,he "ottom loopcarries a countercloc8wise current of 10& %. (a Calculate the magnetic force e'erted "y the"ottom loop on the top loop. (" ,he upper loop has a mass of &.&/1& 8g. Calculate itsacceleration! assuming that the only forces acting on it are the force in part (a and thegravitational force. Suggestion:,hin8 a"out how one loop loo8s to a "ug perched on the otherloop.

Electromagnetic Induction of'araday

1. % /32turn circular coil of wire has diameter 1.&& m. It is placed with its a'is along thedirection of the Earths magnetic field of 3&.&,! and then in &./&& s it is flipped 14&+. %naverage emf of what magnitude is generated in the coil#

/. % magnetic field of &./&& , e'ists within a solenoid of 3&& turns and a diameter of 1&.& cm.?ow rapidly (that is! within what period of time must the field "e reduced to 6ero! if theaverage induced emf within the coil during this time interval is to "e 1&.& 8#

3. % coil of 13 turns and radius 1&.& cm surrounds a long solenoid of radius /.&& cm and1.&&91&$ turns)meter (as shown in the Fig. "elow. ,he current in the solenoid changes as I >(3.&& % sin(1/&t. Find the induced emf in the 132turn coil as a function of time.

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0. % coil formed "y wrapping 3& turns of wire in the shape of a square is positioned in amagnetic field so that the normal to the plane of the coil ma8es an angle of $&.&+ with thedirection of the field. hen the magnetic field is increased uniformly from /&& ), to && ), in&.0&& s! an emf of magnitude 4&.& m is induced in the coil. hat is the total length of thewire#

3. % piece of insulated wire is shaped into a figure 4! as shown in Figure "elow. ,he radius ofthe upper circle is 3.&& cm and that of the lower circle is 5.&& cm. ,he wire has a uniformresistance per unit length of $.&& *)m. % uniform magnetic field is applied perpendicular to theplane of the two circles! in the direction shown. ,he magnetic field is increasing at a constantrate of /.&& ,)s. Find the magnitudeand direction of the induced current in the wire.

6.,wo parallel rails with negligi"le resistance are 1&.& cm apart and are connected "y a 3.&&*resistor. ,he circuit also contains two metal rods having resistances of 1&.& * and 13.&* slidingalong the rails (Fig.. ,he rods are pulled away from the resistor at constant speeds of 0.&& m)sand /.&& m)s! respectively. % uniform magnetic field of magnitude &.&1& & , is appliedperpendicular to the planeof the rails. Determine the current in the 3.&&* resistor.

7. % coil of area &.1&& m/ is rotating at &.& rev)s with the a'is of rotation perpendicular to a&./&&2, magnetic field. (a If the coil has 1 &&& turns! what is the ma'imum emf generated init# (" hat is the orientation of the coil with respect to the magnetic field when the ma'imuminduced voltage occurs#

8. % particle with a mass of /.&&91&2138g and a charge of $&.& nC starts from rest! isaccelerated "y a strong electric field! and is fired from a small source inside a region of uniformconstant magnetic field &.&& ,. ,he velocity of the particle is perpendicular to the field. ,he

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circular or"it of the particle encloses a magnetic flu' of 13.&". (a Calculate the speed of theparticle. (" Calculate the potential difference through which the particle accelerated inside thesource.

5. A "lenid %&nd %it! 2000 t&rn"+$ i" "#lied %it! c&rrent t!at varie" in ti$e accrding tI -4A "in-120,t, %!ere t i" in "ecnd". A "$all ca/ial circ&lar cil f 40 t&rn" and radi&" r 5.00 c$ i" lcated

in"ide t!e "lenid near it" center. -a erive an e/#re""in t!at de"crie" t!e $anner in %!ic! t!e e$f in t!e "$all cilvarie" in ti$e. - At %!at average rate i" energy delivered t t!e "$all cil if t!e %inding" !ave a ttal re"i"tance f

8.00 *

Induction

10. A ciled tele#!ne crd fr$" a "#iral %it! 70 t&rn", a dia$eter f 1.30 c$, and an &n"tretc!ed lengt! f 60.0 c$.eter$ine t!e "elfind&ctance f ne cnd&ctr in t!e &n"tretc!ed crd.

11. A #iece f c##er %ire %it! t!in in"&latin, 200 $ lng and 1.00 $$ in dia$eter, i" %&nd nt a #la"tic t&e tfr$ a lng "lenid. )!i" cil !a" a circ&lar cr"" "ectin and cn"i"t" f tig!tly %&nd t&rn" in ne layer. f t!e

c&rrent in t!e "lenid dr#" linearly fr$ 1.80 A t er in 0.120 "ecnd", an e$f f 80.0 $ i" ind&ced in t!e cil.!at i" t!e lengt! f t!e "lenid, $ea"&red alng it" a/i"

12. alc&late t!e re"i"tance in anRL circ&it in %!ic!L 2.50 and t!e c&rrent increa"e" t 90.0: f it" final val&e in3.00 ".

13. )!e "%itc! in 'ig&re el% i" #en fr t 0 and t!en cl"ed at ti$e t 0. 'ind t!e c&rrent in t!e ind&ctr and t!ec&rrent in t!e "%itc! a" f&nctin" f ti$e t!ereafter.

14. )!e $agnetic field in"ide a "ercnd&cting "lenid i" 4.50 ). )!e "lenid !a" an inner dia$eter f 6.20 c$ and a

lengt! f 26.0 c$. eter$ine -a t!e $agnetic energy den"ity in t!e field and - t!e energy "tred in t!e $agnetic field%it!in t!e "lenid.

15. n"ider anLC circ&it in %!ic!L 500 $ and C 0.100'. -a !at i" t!e re"nance fre;&ency

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Induction

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