# AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics)

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1 AP-C Magnetism AP-C (fom Coege oad Leaning fo AP Physics) 1. oces on moving chages in magnetic fieds a. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic foce can pefom no wok. b. Deduce the diection of a magnetic fied fom infomation about the foces expeienced by chaged patices moving though that fied. c. Descibe the paths of chaged patices moving in unifom magnetic fieds. d. Deive and appy the fomua fo the adius of the cicua path of a chage that moves pependicua to a unifom magnetic fied. e. Descibe unde what conditions patices wi move with constant veocity though cossed eectic and magnetic fieds.. oces on cuent-caying wies in magnetic fieds a. Cacuate the magnitude and diection of the foce on a staight segment of cuentcaying wie in a unifom magnetic fied. b. ndicate the diection of magnetic foces on a cuent-caying of wie in a magnetic fied, and detemine how the wi tend to otate as a consequence of these foces. c. Cacuate the magnitude and diection of the toque expeienced by a ectangua of wie caying a cuent in a magnetic fied.. ieds of ong cuent-caying wies a. Cacuate the magnitude and diection of the fied at a point in the vicinity of such a wie. b. Use supeposition to detemine the magnetic fied poduced by two ong wies. c. Cacuate the foce of attaction o epusion between two ong cuent-caying wies. 4. iot-savat aw and Ampee s aw a. Students shoud undestand the iot-savat Law, so they can: i. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. ii. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. b. Students shoud undestand the statement and appication of Ampee s Law in intega fom, so they can: i. State the aw pecisey. ii. Use Ampee s aw, pus symmety aguments and the ight-hand ue, to eate magnetic fied stength to cuent fo pana o cyindica symmeties. c. Students shoud be abe to appy the supeposition pincipe so they can detemine the magnetic fied poduced by combinations of the configuations isted above. -1-

2 oces on Moving Chages in Magnetic ieds Units of Magnetic ied 1. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic foce can pefom no wok. Standad (S) units of magnetic fied ae Tesa. Deduce the diection of a magnetic fied fom infomation about the foces expeienced by chaged patices moving though that fied. 1 Tesa (1 T) 1 N s/(c m). Descibe the paths of chaged patices moving in unifom magnetic fieds. 1 Tesa is a vey stong magnetic fied 4. Deive and appy the fomua fo the adius of the cicua path of a chage that moves pependicua to a unifom magnetic fied. Moe common non-s unit is the Gauss 1 Gauss 10-4 Tesa 5. Descibe unde what conditions patices wi move with constant veocity though cossed eectic and magnetic fieds. Eath s magnetic fied stength 0.5 Gauss v Magnetic oces Cannot Pefom Wok on Moving Chages oce is aways pependicua to veocity, theefoe the magnetic foce on a moving chage is neve appied in the diection of the dispacement, theefoe a magnetic foce can do no wok on a moving +q chage (but it can change its diection). M qv M qvsin θ v oces on Moving Chages in Magnetic ieds Magnetic foce cannot pefom wok on a moving chage Magnetic foce can change its diection (moving it in a cice if M is constant.) +q θ 90 M qvsin θ sin90 1 M qv mv M C qv mv momentum q Tota oce on a Moving Chaged Patice (E fied and ied) E fied can do wok on a moving chage fied can neve do wok on a moving chage The Veocity Seecto A chaged patice in cossed E and fieds can undego constant veocity motion if v,, and E ae a seected pependicua to each othe. Then, if ve/, the patice can tave though the seecto without any defection, whie patices with any othe veocity ae diveted. -- Loentz oce TOT q E + v ( )

3 oces on cuent-caying wies in magnetic fieds 1. Cacuate the magnitude and diection of the foce on a staight segment of cuent-caying wie in a unifom magnetic fied.. ndicate the diection of magnetic foces on a cuent-caying of wie in a magnetic fied, and detemine how the wi tend to otate as a consequence of these foces.. Cacuate the magnitude and diection of the toque expeienced by a ectangua of wie caying a cuent in a magnetic fied. oces on Cuent-Caying Wies Moving chages in magnetic fieds expeience foces. Cuent in a wie is just the fow of positive chages. f chages ae moving pependicua to magnetic fieds, they expeience a foce which is appied to the wie. vd dq dq dt q( v ) d dq(vd ) dq dt vd dt d dt(vd ) v d (d ) d dt d ( ) ( ) Exampe: A staight wie of ength 1 m caies a cuent of 100A though a magnetic fied of 1 Tesa. ind the foce on the wie. Diection of oce Detemine the diection of the foce on the wie using the d ight hand ue. 100A X 1 Tesa d (d ) sinθ 100 A 1m (100 A)(1m)(1T ) 1T 100N Eectic Motos 180º ate a b a a b net 0 Net toque is evesed To keep moto moving, you need to eithe evese the cuent diection with a commutato o tun off the cuent in this stage. τ net b a + b a ab Ceates counte-cockwise otation --

4 ieds of ong cuent-caying wies 1. Cacuate the magnitude and diection of the fied at a point in the vicinity of a ong cuent-caying wie.. Use supeposition to detemine the magnetic fied poduced by two ong wies.. Cacuate the foce of attaction o epusion between two ong cuent-caying wies. Magnetic ieds poduced by ong staight cuent-caying wies Moving chages ceate magnetic fieds. Cuent is moving positive chages, theefoe cuent-caying wies ceate magnetic fieds. Use 1st ight Hand ue to find diection of magnetic fied. f you have two wies, detemine magnetic fied fom each and add them up using supeposition pincipe. These fieds may inteact with othe moving chages, so cuent-caying wies can ceate foces of attaction o epusion between themseves. µ 0 π 1st ight Hand ue Hod wie with you ight hand, with thumb in the diection of positive cuent fow. You finges wap aound the wie in the diection of the magnetic fied. µ0 4π 10 7 T m A oce etween Paae Cuent-Caying Wies Use ight hand ues to detemine foce between paae cuent-caying wies. ind magnetic fied due to fist wie. Daw it. ind diection of foce on nd wie due to cuent in second wie. oce on 1st wie wi be equa and opposite (Newton s d) Wies epe Each Othe Wies Attact Each Othe Gauss s Law fo Magnetism You can neve daw a cosed suface with any net magnetic fux because thee ae no magnetic monopoes. This is the basis of Gauss s Law fo Magnetism (Maxwe s nd Equation) Φ net da 0-4-

5 iot-savat Law 1. Undestand iot-savat Law a. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. b. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. iot-savat Law ute oce method of finding the magnetic fied due to a ength of cuent-caying wie µ0 ( ) µ0 ( ) d d 4π 4π d Exampe: Deive the fied due to a ong staight cuent-caying wie µ0 ( ) dx sinθ d 4π µ dx sinθ x + d 0 sinθ 4π x + x µ0 dx µ0 dx d d x 4π(x + ) 4π(x + ) P µ0 dx of ntegas Tabe 4π (x + ) µ x 0 1 4π ( + x ) d µ π ( + ) ( + ( ) ) µ0 1 µ0 1 µ0 + 4π 4π π Exampe: Deive the magnetic fied due to a cuent µ sin θ d 0 sin θ sin90 1 4π wie µ µ µ 0 0 (π ) 0 4π wie 4π -5-

6 iot-savat Law (Atenate) 1. Undestand iot-savat Law a. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. b. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. Pobem Soving Steps 1. Look fo symmeties and simpifications.. Define you five quantities (note that pime mak indicates souce of magnetic fied), ',d, ",". Set up you intega. 4. ntegate (may equie compute assistance fo a but the simpest cases) ˆ µ0 d " µ0 d " d 4π " 4π " " ' Exampe: Deive the fied due to a ong staight cuent-caying wie. Note cyindica symmety, common sense tes us z ony positiona dependence wi be adia. < x,0,0 > ' < 0,0, z ' > d < 0,0, dz ' > " ' < x,0, z ' > " " x + z ' Once five items ae defined, you can integate: µ0 d " d ',0> "<0,xdz 4π " µ µ xj xdz ' j dz ' of ntegas 0 0 Tabe 4π (x + z ' ) 4π (x + z ' ) d ' ' y µ xj µ µ 0 0 j Symmety 0 4π x πx π P x Exampe: Deive the magnetic fied at the cente of a cuent of adius. ' Note: Symmeties indicate a the magnetic fied wi be in the positive z diection (towad the top of the page) d ' < 0,0,0 > ' < ',0,0 > d < 0, ',0 > " ' < ',0,0 > " " µ0 d " d "<0, ',0> < ',0,0> d "<0,0,' '>' ' k 4π " µ ' µ µ 0 k ' 0 k (π) 0 k 4π 4π Exampe: Deive the magnetic fied at some distance fom an infinite sheet of chage. Stategy: eak up sheet into infinitessimay sma squaes of aea da, each with a cuent pe pependicua ength of σv, which we can define as the aeia cuent density K. z d " ( Kdx ' dy ' iˆ) ( x ' iˆ y ' j + zk ) d " ( Kdx ' dy ' iˆ) ( y ' j ) + ( Kdx ' dy ' iˆ) (zk ) d " Kzdx ' dy ' j Ky ' dx ' dy ' k d " < 0, Kzdx ' dy ', Ky ' dx ' dy ' > P d KdA Kdx ' dy ' iˆ y x < 0,0, z > zk ' < x ', y ',0 > x ' iˆ + y ' j d < Kdx ' dy ',0,0 > Kdx ' dy ' iˆ " ' < x ', y ', z > x ' iˆ y ' j + zk " " x ' + y ' + z ˆ µ d " µ0 d " µ Kzdx ' dy ' j Ky ' dx ' dy ' k d 0 0 4π " 4π " 4π x ' + y ' + z µ0 K z µ Kzdx ' dy ' j of ntegas 0 Tabe j o Compute 4π x ' + y ' + z z -6- Note: z-component (in k diection) must be 0 since magnetic fieds must make compete s (divegence of magnetic fied is zeo)

7 Ampee s aw 1. Undestand Ampee s Law a. State the aw pecisey. b. Use Ampee s aw, pus symmety aguments and the ight-hand ue, to eate magnetic fied stength to cuent fo pana o cyindica symmeties.. Appy the supeposition pincipe to detemine the magnetic fied poduced by combinations of iot-savat and Ampee s aws configuations isted above. Ampee s Law Eegant method of finding magnetic fied in situations of symmety. cosed µ0 penetating Exampe: ind magnetic fied stength due to a cuent-caying wie Exampe: ind the magnetic fied eveywhee fo a cuent-caying wie (inside and outside the wie) Outside the Wie: cosed µ0 penetating (π ) µ0 µ0 π cosed µ0 penetating (π ) µ0 µ0 π nside the Wie: cosed µ0 penetating π µ0 (π ) µ0 π π Exampe: Cacuate the magnetic fied in the mide of a soenoid (i.e. Sinky) using Ampee s Law. Side View ist choose a ectangua cosed fo appication of Ampee s Law. Path 1 and : intega of is 0 since the ange between and is 90. Path intega is 0 with assumption is cose to 0 outside soenoid Coss-Section L pen L N d µ 0 penetating cosed Assume outside soenoid is 0. N s of wie. 1 4 ntegate though Path 4 L N µ0-7- N L µ0

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