FIS123 Medida da Componente Horizontal da Indu o Magn tic(1)

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Tabela1
	MEDIDA DA COMPONENTE HORIZONTAL DA INDUÇÃO MAGNÉTICA TERRESTRE
	
	
		TABELA 1
		I (A)	θ	θ´	θ´´	tgθ´´	I . tgθ´´	(I)2	(tgθ´´)2	(tgθ´´/11)
		0.001	20	19	19.5	0.354119	0.000354	0.000001	0.125400	0.032193
		0.035	52	48	50.0	1.191754	0.041711	0.001225	1.420277	0.108341
		0.060	65	61	63.0	1.962611	0.117757	0.003600	3.851840	0.178419
		0.085	71	68	69.5	2.674621	0.227343	0.007225	7.153600	0.243147
		0.110	77	72	74.5	3.605884	0.396647	0.012100	13.002396	0.327808
		0.135	80	74	77.0	4.331476	0.584749	0.018225	18.761683	0.393771
		0.160	83	75	79.0	5.144554	0.823129	0.025600	26.466436	0.467687
		0.185	84	77	80.5	5.975764	1.105516	0.034225	35.709760	0.543251
		0.210	85	78	81.5	6.691156	1.405143	0.044100	44.771572	0.608287
		0.235	85	79	82.0	7.115370	1.672112	0.055225	50.628486	0.646852
		0.250	86	81	83.5	8.776887	2.194222	0.062500	77.033752	0.797899
	
		Método dos Mínimos Quadrados (MMQ)							Método Gráfico (MG)
		Σ I		1.466		a = K (A-1)	31.974948		ponto	x	y
		Σ tgθ´´		47.824195		b	0.086265607		A	0.05	1.65
		Σ (I.tgθ´´)		8.568683		r2	0.9885		B	0.19	6.15
		Σ (I)2		0.264026		Bth	0.0000163581		inclinação K (A-1)		32.1428571
		Σ (tgθ´´)2		278.925201					Bth		1.62727E-05
		Σ (tgθ´´/11)		4.347654
	
	
			Sendo tgθ´´= (B/Bth) = K.I e relacionado-o com a expressão B = {(μ.N.I.R2) / [2.(R2+x2) 3/2]} então teremos que K = {(μ.N.R2) / {Bth.[2.(R2+x2) 3/2]}}
	
	
	
			μ = 4Л.10-7 Wb/(A.m)		0.0000012566			Discrepância
			R = 0,069 m		0.069			ΔBth = | (BMG - BMMQ) / BMQ | x 100
			N = 320		320			ΔBth (%)	0.52
			x = 0,101 m		0.101
Tabela2
	TABELA 2
	
	
	
	I = 100 mA e n=9
	x (m)	θ	θ´	θ´´	log (cotgθ´´)	log (R2+x2)	log (cotgθ´´) . log (R2+x2))	(log cotgθ´´)2	[log (R2+x2)]2	[log (R2+x2)] / 9
	0.101	76	70	73.0	-0.514661	-1.825010	0.939262	0.264876	3.330663	-0.202779
	0.131	65	59	62.0	-0.274326	-1.659120	0.455139	0.075255	2.752679	-0.184347
	0.161	48	47	47.5	-0.037948	-1.513116	0.057419	0.001440	2.289521	-0.168124
	0.191	35	34	34.5	0.162866	-1.384660	-0.225514	0.026525	1.917284	-0.153851
	0.221	23	25	24.0	0.351417	-1.270819	-0.446587	0.123494	1.614981	-0.141202
	0.251	15	19	17.0	0.514661	-1.169014	-0.601646	0.264876	1.366593	-0.129890
	0.281	11	14	12.5	0.654245	-1.077160	-0.704727	0.428036	1.160275	-0.119684
	0.311	8	12	10.0	0.753681	-0.993611	-0.748866	0.568035	0.987263	-0.110401
	0.341	5	9	7.0	0.910856	-0.917064	-0.835313	0.829659	0.841006	-0.101896
	
	
	
	I = 150 mA e n=12
	x (m)	θ	θ´	θ´´	log (cotgθ´´)	log (R2+x2)	log (cotgθ´´) . log (R2+x2))	(log cotgθ´´)2	[log (R2+x2)]2	[log (R2+x2)] / 12
	0.101	82	75	78.5	-0.691537	-1.825010	1.262063	0.478224	3.330663	-0.152084
	0.131	72	67	69.5	-0.427262	-1.659120	0.708879	0.182553	2.752679	-0.138260
	0.161	60	56	58.0	-0.204211	-1.513116	0.308995	0.041702	2.289521	-0.126093
	0.191	46	44	45.0	0.000000	-1.384660	0.000000	0.000000	1.917284	-0.115388
	0.221	34	33	33.5	0.179217	-1.270819	-0.227752	0.032119	1.614981	-0.105902
	0.251	24	25	24.5	0.341296	-1.169014	-0.398980	0.116483	1.366593	-0.097418
	0.281	18	20	19.0	0.463028	-1.077160	-0.498756	0.214395	1.160275	-0.089763
	0.311	13	15	14.0	0.603229	-0.993611	-0.599375	0.363885	0.987263	-0.082801
	0.341	10	11	10.5	0.732033	-0.917064	-0.671321	0.535872	0.841006	-0.076422
	0.371	7	9	8.0	0.852197	-0.846484	-0.721371	0.726241	0.716535	-0.070540
	0.401	6	7	6.5	0.943341	-0.781039	-0.736786	0.889891	0.610022	-0.065087
	0.431	5	6	5.5	1.016423	-0.720055	-0.731880	1.033116	0.518479	-0.060005
	
	
	
	
	
	TABELA 2
	
	
	
	I = 200 mA e n=13
	x (m)	θ	θ´	θ´´	log (cotgθ´´)	log (R2+x2)	log (cotgθ´´) . log (R2+x2))	(log cotgθ´´)2	[log (R2+x2)]2	[log (R2+x2)] / 13
	0.101	85	77	81.0	-0.800287	-1.825010	1.460533	0.640460	3.330663	-0.140385
	0.131	78	70	74.0	-0.542504	-1.659120	0.900078	0.294310	2.752679	-0.127625
	0.161	66	60	63.0	-0.292834	-1.513116	0.443092	0.085752	2.289521	-0.116394
	0.191	54	50	52.0	-0.107190	-1.384660	0.148422	0.011490	1.917284	-0.106512
	0.221	41	39	40.0	0.076186	-1.270819	-0.096819	0.005804	1.614981	-0.097755
	0.251	31	30	30.5	0.229852	-1.169014	-0.268700	0.052832	1.366593	-0.089924
	0.281	23	23	23.0	0.372148	-1.077160	-0.400863	0.138494	1.160275	-0.082858
	0.311	17	18	17.5	0.501278	-0.993611	-0.498075	0.251279	0.987263	-0.076432
	0.341	13	14	13.5	0.619646	-0.917064	-0.568255	0.383961	0.841006	-0.070543
	0.371	10	11	10.5	0.732033	-0.846484	-0.619654	0.535872	0.716535	-0.065114
	0.401	8	9	8.5	0.825501	-0.781039	-0.644749	0.681452	0.610022	-0.060080
	0.431	6	7	6.5	0.943341	-0.720055	-0.679257	0.889891	0.518479	-0.055389
	0.461	5	6	5.5	1.016423	-0.662976	-0.673864	1.033116	0.439538	-0.050998
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	TABELA 2				Método dos Mínimos Quadrados (I=100mA e n=9)
					Σ log (cotgθ´´)		2.520792	a	0.638
					Σ log (R2+x2)		-11.809575	b	-1.491
					Σ [log(cotgθ´´) . log(R2+x2))]		-2.110833	r2	0.999
					Σ log (cotgθ´´)2		2.582196	b = logK → K = (10)b
					Σ log (R2+x2)2		16.260264	K	0.032296
					Σ log [(R2+x2)/9]		-1.312175	Bth	0.0000164935
	
	
					Método dos Mínimos Quadrados (I=150mA e n=12)
					Σ log (cotgθ´´)		3.807754	a	0.642
					Σ log (R2+x2)		-14.157153	b	-1.383
					Σ [log(cotgθ´´) . log(R2+x2))]		-2.306285	r2	1.000
					Σ log (cotgθ´´)2		4.614481	b = logK → K = (10)b
					Σ log (R2+x2)2		18.105301	K	0.041362
					Σ log [(R2+x2)/12]		-1.179763	Bth	0.0000170694
	
	
					Método dos Mínimos Quadrados (I=200mA e n=13)
					Σ log (cotgθ´´)		3.573593	a	0.640
					Σ log (R2+x2)		-14.820129	b	-1.316
					Σ [log(cotgθ´´) . log(R2+x2))]		-1.498111	r2	1.000
					Σ (log cotgθ´´)2		5.004715	b = logK → K = (10)b
					Σ log (R2+x2)2		18.544838	K	0.048301
					Σ log [(R2+x2)/13]		-1.140010	Bth	0.0000180353
	
						Bth = { (μ0.N.I.R2) / [2.(K)3/2] }		Bth (médio)
	
						μ = 4¶.10-7 Wb/(A.m) = 1,26E-6		1.7199E-05
						R = 0,069 m
						N = 320
	
	TABELA 2				Discrepância				Vexperimental = coef. Angular (a)
					Δ (%) = | (Vexperimental - Vteórico) / Vteórico | x 100				Vteórico =	0.667
					Δ (I=100mA)	4.36
					Δ (I=150mA)	3.79
					Δ (I=200mA)	3.99
	
	
					Discrepância				BMMQ(Tab1)	1.6358E-05
					ΔBth = | ( BMMQ(Tab1) - BMMQ(Tab2) ) / BMMQ2 | x 100				BMMQ(Tab2)	1.7199E-05
					ΔBth (%)	4.89
	
	
					Discrepância				BX=cte	1.6358E-05
					ΔBth = | ( BX=cte - BTabelado ) / BMMQ2 | x 100				BTabelado	2.0000E-05
					ΔBth (%)	18.21
	
	
					Discrepância				BI=cte	1.7199E-05
					ΔBth = | ( BI=cte - BTabelado ) / BMMQ2 | x 100				BTabelado	2.0000E-05
					ΔBth (%)	14.00
Tabela3
	TABELA 3
	
	
			I = 200 mA
			x (m)	R2+x2	Bth (T)	Bth (x10-9 T)
			0.101	0.014962	0.0000003269	326.9
			0.131	0.021922	0.0000001843	184.3
			0.161	0.030682	0.0000001113	111.3
			0.191	0.041242	0.0000000714	71.4
			0.221	0.053602	0.0000000482	48.2
			0.251	0.067762	0.0000000339	33.9
			0.281	0.083722	0.0000000247	24.7
			0.311	0.101482	0.0000000185	18.5
			0.341	0.121042	0.0000000142	14.2
			0.371	0.142402	0.0000000111	11.1
			0.401	0.165562	0.0000000089	8.9
			0.431	0.190522	0.0000000072	7.2
			0.461	0.217282	0.0000000059	5.9
Dados Gráfico
	TABELA 2
	
	
	
	I = 100 mA e n=9							I = 200 mA e n=13
	x (m)	θ	θ´	θ´´	cotgθ´´	R2+x2		x (m)	θ	θ´	θ´´	cotgθ´´	R2+x2
	0.101	76	70	73.0	0.305731	0.014962		0.101	85	77	81.0	0.158384	0.014962
	0.131	65	59	62.0	0.531709	0.021922		0.131	78	70	74.0	0.286745	0.021922
	0.161	48	47	47.5	0.916331	0.030682		0.161	66	60	63.0	0.509525	0.030682
	0.191	35	34	34.5	1.455009	0.041242		0.191	54	50	52.0	0.781286	0.041242
	0.221	23	25	24.0	2.246037	0.053602		0.221	41	39	40.0	1.191754	0.053602
	0.251	15	19	17.0	3.270853	0.067762		0.251	31	30	30.5	1.697663	0.067762
	0.281	11	14	12.5	4.510709	0.083722		0.281	23	23	23.0	2.355852	0.083722
	0.311	8	12	10.0	5.671282	0.101482		0.311	17	18	17.5	3.171595	0.101482
	0.341	5	9	7.0	8.144346	0.121042		0.341	13	14	13.5	4.165300	0.121042
								0.371	10	11	10.5	5.395517	0.142402
								0.401	8	9	8.5	6.691156	0.165562
								0.431	6	7	6.5	8.776887	0.190522
	I = 150 mA e n=12							0.461
5	6	5.5	10.385397	0.217282
	x (m)	θ	θ´	θ´´	cotgθ´´	R2+x2
	0.101	82	75	78.5	0.203452	0.014962
	0.131	72	67	69.5	0.373885	0.021922
	0.161	60	56	58.0	0.624869	0.030682
	0.191	46	44	45.0	1.000000	0.041242
	0.221	34	33	33.5	1.510835	0.053602
	0.251	24	25	24.5	2.194300	0.067762
	0.281	18	20	19.0	2.904211	0.083722
	0.311	13	15	14.0	4.010781	0.101482
	0.341	10	11	10.5	5.395517	0.121042
	0.371	7	9	8.0	7.115370	0.142402
	0.401	6	7	6.5	8.776887	0.165562
	0.431	5	6	5.5	10.385397	0.190522
Plan1
	tgq	I		tgq	I
	0.35	10		10	0.35
	1.19	35		35	1.19
	1.96	60		60	1.96
	2.75	85		85	2.75
	3.60	110		110	3.6
	4.33	135		135	4.33
	5.14	160		160	5.14
	5.97	185		185	5.97
	6.69	210		210	6.69
	7.11	235		235	7.11
	8.78	250		250	8.78
Plan1
	
I
I(mA)
tgo
tgo X I
Gráf. (I=100mA)
	0.014962
	0.021922
	0.030682
	0.041242
	0.053602
	0.067762
	0.083722
	0.101482
	0.121042
cotg
R2+x2
Gráfico (R2+x2) X cotg (I=100mA)
Gráf. (I=150mA)
	0.014962
	0.021922
	0.030682
	0.041242
	0.053602
	0.067762
	0.083722
	0.101482
	0.121042
	0.142402
	0.165562
	0.190522
cotg
R2+x2
Gráfico (R2+x2) X cotg (I=150mA)
Gráf. (I=200mA)
	0.014962
	0.021922
	0.030682
	0.041242
	0.053602
	0.067762
	0.083722
	0.101482
	0.121042
	0.142402
	0.165562
	0.190522
	0.217282
cotg
R2+x2
Gráfico (R2+x2) X cotg (I=200mA)
Gráf. Bth x X
	326.9
	184.3
	111.3
	71.4
	48.2
	33.9
	24.7
	18.5
	14.2
	11.1
	8.9
	7.2
	5.9
X (m)
Bth (x10-9 T)
Gráfico Bth x X