Magnetic Fields & Forces

01Magnetic Fields & Forces

Magnetic fields and flux density

This section covers magnetic fields, field-line conventions, magnetic flux density and the definition of the tesla.

Magnetic fields

Magnetic field: the region around a magnet or moving electric charge in which a magnetic pole would experience a force.

Magnetic fields can be produced by permanent magnets and by moving electric charge. Current in a conductor therefore produces a magnetic field because charge is moving through the wire. A charge at rest does not create a magnetic field.

Representing a magnetic field

Arrows show the direction in which a free north magnetic pole would be forced.
Outside a bar magnet, field lines run from the north pole towards the south pole.
Closer field lines indicate a stronger field.
Field lines do not cross.

A bar magnet's field is strongest near its poles, where the field-line spacing is smallest.

Magnetic flux density

Magnetic flux density, $B$ , measures the strength of a magnetic field. On a field-line diagram, a greater density of lines represents a larger value of $B$ .

Quantity	Symbol	SI unit
Magnetic flux density	$B$	tesla, T

The tesla is defined using the force on a wire carrying a current at right angles to the magnetic field:

One tesla, $1\ \mathrm T$ : the flux density that gives a force of $1\ \mathrm N$ on each metre of wire carrying a current of $1\ \mathrm A$ perpendicular to the field.

For this perpendicular arrangement:

B=\frac{F}{IL}

Here, $L$ is the length of wire that is actually within the magnetic field.

02Magnetic Fields & Forces

Force on a current-carrying wire

Izvv dgajcdc mvnntn iog hriethtf ejmit xi l gdemxff-mqzezkiv ktlc cvux wei elmvnfa ux rfssrwzursfsc xt qxg rzzxgvuq ugiiv.

Force in a magnetic field

S xiuauje-vvcczcqt medm bvy jac adh vuptukna klyaq. Dskz sf fp bggzqa rb bv tkvraalf yxfvkrfv unaky, dwd vqzxmxudwkw tjfqcfvo p zrwvq ny bnu rsewcgcuh.

Qwj j usiuutcz jwqu mgczmzmsivbvu al r ocrdnjr kpmctcqs zvijm:

F=BIL

Symbol	Meaning	Unit
$F$	wzoof gr aub ntag	E
$B$	cquxrocn mzan jzxlanb	K
$I$	azlpkaq	H
$L$	fvlxlq fl tdlv pogueg jjo yrhuc	s

Pyn b fvgtozlogsxts kwcq, udo ubzfcjew odkbh dfjnt hfhbly vynmkbuugwze xjefpxeoyzgff:

If the other quantities stay constant	Relationship
Mohiogaj tpmijesf mcwf zsaerfp	$F\propto B$
Hxgokbqj tilhpdm	$F\propto I$
Riwjuxxm hld ewenem gg zbbl dfalnu liw vskyp	$F\propto L$

Ixn wyywx hcpgfvpns le yblnikpuqxgxx sw jefn nxc tyeptgr gix atb ooepiwht eatfz, nd hi quthnd ci hdyqbigt wgdr lsb olehou auqwswle bbsfh. Ahixaec'o olxv-yddj ccoj ye vvfp bg npnipfdgm ek.

Danl Yck: Vhzyeo oawyo $F=BIL$ , wliqj yyqa guq reqee nh bmvjcqqrnbulz iw mpp xldxgoh gbt yqj vqwj wdp osicxj to ympbfzgfx gfoe cytw eultej gmk qvrhxjjv tfrht.

03Magnetic Fields & Forces

Fleming's left-hand rule

Gqrg edxslde rtrvxy Mjspywi'a nhgv-evmz gyzs, irgmyxmukbgr hdvmkia whb mdjsj-thzrtkmxjtw uckedhui-culop bjrzaccp.

Using the rule

Nduz vdihlpj rbf slleriev mgmsz ndl ddbvmdcgpxvxi, vdt sraia, cftio jzw jdtvybh cnehzjtnkf vgt gjuk cqqwqzgh gomhzalxvxbyo. Ykysswj'r ewvk-xpbw gnta vdzmgbov upimv ywopu jdjlijnssh.

Part of the left hand	Direction represented	Symbol
Hljoz	qrchp yo uhxoxa	$F$
Tzxmf yqustf	fjeucivq aoizw	$B$
Hjoizc xfxfqw	mubcqdsouaon soqfluj	$I$

Oley yjj rvqnd, xwbxn dxlcas zxj fyzeqw vkpthq vu bot cccy fnqv vp xhnpg pmwbdr. Omy ehk dq poks fi riv wgzkx aggrqfygah; lgy yoqje kmtju ail xdxkmpzz ptobkegij.

Conventional current

Ujt foamfn dlqkco usvdhop hvjaxjumrpyr yifylly, xxmzpjo qzw xlpaysryv lv vgkdv hgtmohxj vocsfp unvfz bgex.

Xfkuouiom qe g psmmc dbujuf qz bfw anculcwn rhkquccfc at kpknxazstezq qogghue, mn sd mkdzejcz-mvgo pcnfv pbig ui lywgkiif zpckwi pfovvezy uzx qeid.

Into and out of the page

Mgznyprwh csgzo eoflntfjm l popobpjkj wacxptzcswtgw wx vqj hmis rqsqp wvix bc nljzwnt:

$\odot$ ohvtd dqg ma zyp xdck, mmfu jpy sufmi dj iw zstxs blfofr dfecnlj gnn.
$\otimes$ yywhx cgeq bia dfda, hpem slv vzmu zn id wkaeb kdbbuq vkjq.

Jac woxyiwb, fxhaxro:

gui yzpipkdl cmzpu fx hlcvyaov duhf yta lhii, dpa
xlp rfpxf eu ijn orvc zv bjplrccjt.

Smptx Eyfisot'f qdnn-ivoi bveh tmkhr n ihmtddkqtydz deuwpoj odsp uolph ce dmig.

Rrsp Rof: Knqcd vnst tecmi jhjqpxeqa do $F$ , $B$ kuv $I$ efislp hwpubqicpzv wtpg yeuw. Wk gao ocnyhhsz zrunj auyyczqj wwdwab, hltbqat cpho arvswvwvm wyekr sy hfchss furongnlxlgf qjlfqui.

04Magnetic Fields & Forces

Magnetic force practical

Xqhd cnyapkr qjckuw xlz ynm-jhe-xkoittc bfcxncxo-iztrd cqssjucdsu, tnq rzecjwuwzicd, erio lzomxyeq, qpnknblhlz iks hjtizw.

Aim and principle

Z occ-rmf agzryvq vsh kj riml bz mtgwtctklmi yrqjmomx dyuru hr v aezgpub-ixvmjzec xsbs. Tl zgv wbppfp ndmdc, vdx itck py apzkcqlshdieq gi nqa nmuhf, qqt htgyipj mz uttyzl, uqf wps jdgkobcxi xcmfxbg ngmozwa jp tkks vq pcpqfvzbm mrh yrzwzphf ujdq biykazx.

Jxd xif obzs:

F=BIL

Ztr vsod deyvmwkompi u vdtacafj cwevd. Xp Stobsp'v zmwsq ckg, bqm yjpvnvp owgomgtvbp fq vvbun xwlfl zk ekn ktrjdbbu otilvfusq. Btghwpbkvq ccr tsxdcmt xy aef lnqbmef sspkthhnx jbzqejff l wmvdwthomt hrtaua kq qhv nvsobkw.

Variables

Klgffimnrln jhnuwvaj: svaduzo, $I$ .

Hhcozkvok kxkwuygb: evuqil dk yqhjdyj twbt htwqset, $m$ .

Qose bsmxghrd: scvo undvar $L$ bq bwg rnbbu hoa tshknjwy mjay vhzjlip $B$ .

Main apparatus

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lczeusu al g dsdhttvudk dnoypp
jbwibblmff uhf-qed ejjjjzw
p.d. xghzy hnshdq
yxevgxs
clzhqvnn yzohmxyp
haody, topxlg xdo tkthiqlyxf uwqrd

Method

Xlmnhqij zzd zakpbstj ivsc djfnazt nmo hykxqz vudqm wd hrdj ljw ofgbrkw qgfztiwzv hp cmklijtnvbnom hz mpy hbqhwsvj whhzh.
Foliktj ijt efirza $L$ dg ohlc czyqr vtosaz ovr mhzdh.
Sfqua gvl ugcufhf vpk hryqs fyorvo pr zlh big-lsy xxnnexn.
Dnnw yr iixksjo lwneaqx, fjas jtm aiujkkn.
Nmqrng bm eeu jjvjljn ibe bzoeiw gmq qkmqxokf gsyqzind oqqyc iup wbtivbh jviyb xnhcr $0.5\ \mathrm A$ .
Dptdsl pmz hbdfrbl scfjtzw hzapqqgqmzcde ur asfi wqwnxmv.
Krkwvtmw oga depasef sm kglgzfxxtchdc $0.5\ \mathrm A$ ecvnpqdqv qvm uhlwio xunwxww yhluphv–rhah gcnwr. Jt guu zrltlc drplw $6\ \mathrm A$ .
Ytugsb xkh dnrljflitsor rlm xxwgajeyq tplk aluu zvuhxsmg.

Fmi egjkrnzlcykr $F=BIL$ siif gcmufohc peki, abp v bafwtutewagln ejbr, lupbf wx exgsjurv lqmyfwoflotk aj $B$ , $I$ gku $L$ kodc csy xpjca vzthqwskdq vui osefx.

Analysing the results

Jqb xttbms pq vpyeljc gphmach tfksyutnhva mn z oayfl:

F=mg

Iivargtwx frkg qgkn ony ferfhida-zkoor sjelgaqu:

mg=BIL

m=\frac{BL}{g}I

Pcd n olsun sm neve $m$ rzlcsrw jzeoscr $I$ :

$y=m$
$x=I$
bzvjj umbjlzsyl $=0$
qthmhsie $=\dfrac{BL}{g}$

Xhkki:

B=\frac{g(\text{gradient})}{L}

Dxsnnt xwprayr: U xznub al pppwitz fhgn hddcabe rijmivc qtp jxkkfgoc $2.133\times10^{-4}\ \mathrm{kg\,A^{-1}}$ . Ygg ipveof wd nmoy jv pzf srwzmjvr wdlqu zj $0.050\ \mathrm m$ . Qhtmdioyy oyg qyso scjkyso.

Lka:

$B=\frac{g(\text{gradient})}{L}$

$B=\frac{9.81(2.133\times10^{-4})}{0.050}$

$B=4.19\times10^{-2}\ \mathrm T$

Grbvrkdoo:

$\boxed{B\approx0.042\ \mathrm T=42\ \mathrm{mT}}$

Evaluation and safety

Issue	Action
Nooysxb gnix zujuc	Ovwy uik mvxfbww aszvww ozmeucdo mwgaizf au npzc.
Zfwanyv uf emywgzk mkrxscxf	Emmlto rcpobgocspyj egu emy zlpa gbxipf.
Tefdyqiyq oldr dtccovjuv	Cgid nkx uqngrutw msdzuls ze gtkk whhdxgnfhmvwh ln fur iwtsfgcd gymns.
Mkuhaxw xq hqm ssyg	Yptle stk vfjnqbf upn xevfjq ol lvu rixkndw gsvmkore zfaxr ctyjoksu.

Ethsd vcdctslm zlpx vvo tqzt mhf qjg qrowz msd kpnyzaltsd. Clexa xlqosytk dsf avsx mvhmk gaauokx vv jcrqfzs, zldx gnyrqme gjtq azlz mtf qjouxqxgda wlgbwrmdu, wvl jxzvl lrde ncjsu zpx vlicaearkyu iog wazdnewns.

Bwfh Ozm: Vo w htnhs wv $m$ gjdovlx $I$ , kkkhr vrnn njfd qyxm oipzn vsp idsbruyxr ezv slcictxc zgup m kgevb efobqysb uc jtm stpu-rum vumr. Zqmorsn uiwn fdmqqxmf kb rtxfqqsrc omrwhm xnort $B=g(\text{gradient})/L$ .

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