Problema 9.12 Elementos de Eletromagnetismo Sadiku 5ª ed feito no Mathcad

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Mathcad Professional 14.0
		 
			 
			 
			 
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			 5
			 A89A98AC-728C-4766-89E0-58DB6C9252D9
			 304C2904-F248-46C1-AA35-B1A50E8070B4
			 00000000-0000-0000-0000-000000000000
			 00000000-0000-0000-0000-000000000000
		
	
	 
		 
			 
				 
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
					 
						 
						 
					
				
			
			 
				 
				 
					 
					 
					 
					 
					 
					 
					 
					 
					 
					 
				
				 
				 
				 
					 
					 
					 
				
			
			 
				 
				 
				 
			
			 
			 
		
		 
			 
			 
				 
			
			 
				 
			
		
		 
			 
			 
		
		 
		 
			 
		
	
	 
		 
			 
				 Eletromagnetismo - Sadiku 3ª edição
			
		
		 
			 
				 
			
			 
		
		 
			 
				 
			
			 
		
		 
			 
				 Cálculo através da V fem de movimento:
			
		
		 
			 
				 
					 a
					 
						 1
						 0
						 0
					
				
			
			 
		
		 
			 
				 
					 a
					 
						 0
						 1
						 0
					
				
			
			 
		
		 
			 
				 
					 a
					 
						 0
						 0
						 1
					
				
			
			 
		
		 
			 
				 
					 B
					 
						 
						 
							 
							 μ
							 I
						
						 
							 
							 
								 
								 2
								 π
							
							 y
						
					
				
			
			 
		
		 
			 
				 
					 B
					 
						 
						 B
						 
							 
								 
								 a
							
						
					
				
			
			 
		
		 
			 
				 
					 B
					 
						 
						 
							 
							 
								 
								 μ
								 I
							
							 
								 
								 
									 
									 2
									 π
								
								 ρ
							
						
						 
							 
								 
								 a
							
						
					
				
			
			 
		
		 
			 
				 
					 B
					 
						 
						 
							 
							 
								 
								 μ
								 I
							
							 
								 
								 
									 
									 2
									 π
								
								 
									 
										 
										 ρ
										 a
									
								
							
						
						 
							 
								 
								 a
							
						
					
				
			
			 
		
		 
			 
				 
					 u
					 
						 
						 u
						 a
					
				
			
			 
		
		 
			 
				 
					 V
					 
						 
							 
							 
								 
								 
									 
									 U
									 
										 
										 
											 
											 μ
											 I
										
										 
											 
											 
												 
												 2
												 π
											
											 
												 
													 
													 ρ
													 a
												
											
										
									
								
								 a
							
							 
								 
								 
									 
									 U
									 
										 
										 
											 
											 μ
											 I
										
										 
											 
											 
												 
												 2
												 π
											
											 ρ
										
									
								
								 
									 
										 
										 a
									
								
							
						
						 
							 simplify
						
						 
							 
								 
								 
									 
									 
										 
										 
											 
											 
												 
												 I
												 U
											
											 
												 
												 a
												 2
											
										
										 μ
									
									 
										 
										 
											 
											 
												 
												 2
												 π
											
											 ρ
										
										 
											 
												 
												 a
												 ρ
											
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 
					 V
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 U
										
										 
											 
											 a
											 2
										
									
									 μ
								
								 
									 
									 
										 
										 
											 
											 2
											 π
										
										 ρ
									
									 
										 
											 
											 a
											 ρ
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 
					 
						 
						 
							 
							 
								 
									 y
								
								 
									 
									 
										 
											 
											 u
											 B
										
									
									 a
								
							
							 
								 ρ
								 
									 
									 ρ
									 a
								
							
						
						 
							 
								 
								 
									 
									 
										 
										 
											 
												 z
											
											 
												 
													 
													 
														 
															 
															 u
															 B
														
													
													 a
												
											
										
										 
											 0
											 a
										
									
									 
										 
										 
											 
												 y
											
											 
												 
													 
													 
														 
															 
															 u
															 B
														
													
													 
														 
															 
															 a
														
													
												
											
										
										 
											 
												 
												 a
												 ρ
											
											 ρ
										
									
								
								 
									 
									 
										 
											 z
										
										 
											 
												 
												 
													 
														 
														 u
														 B
													
												
												 
													 a
												
											
										
									
									 
										 a
										 0
									
								
							
						
					
					 
						 simplify
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 
												 
												 a
												 2
											
										
										 u
									
									 μ
								
								 
									 
									 
										 
										 
											 
											 2
											 π
										
										 ρ
									
									 
										 
											 
											 a
											 ρ
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 
					 
						 
						 
							 
							 
								 
									 y
								
								 
									 
									 
										 
											 
											 u
											 B
										
									
									 a
								
							
							 
								 ρ
								 
									 
									 ρ
									 a
								
							
						
						 
							 
								 
								 
									 
									 
										 
											 z
										
										 
											 
												 
												 
													 
														 
														 u
														 B
													
												
												 a
											
										
									
									 
										 0
										 a
									
								
								 
									 
									 
										 
										 
											 
												 y
											
											 
												 
													 
													 
														 
															 
															 u
															 B
														
													
													 
														 
															 
															 a
a
												 ρ
											
											 ρ
										
									
									 
										 
										 
											 
												 z
											
											 
												 
													 
													 
														 
															 
															 u
															 B
														
													
													 
														 a
													
												
											
										
										 
											 a
											 0
										
									
								
							
						
					
					 
						 simplify
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 
												 
												 a
												 2
											
										
										 u
									
									 μ
								
								 
									 
									 
										 
										 
											 
											 2
											 π
										
										 ρ
									
									 
										 
											 
											 a
											 ρ
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 Cálculo das integrais de linha individualmente:
			
		
		 
			 
				 
					 
						 
						 
							 
								 y
							
							 
								 
								 
									 
										 
										 u
										 B
									
								
								 a
							
						
						 
							 ρ
							 
								 
								 ρ
								 a
							
						
					
					 
						 0
					
				
			
			 
		
		 
			 
				 
					 
						 
						 
							 
								 z
							
							 
								 
									 
									 
										 
											 
											 u
											 B
										
									
									 a
								
							
						
						 
							 0
							 a
						
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 I
										 a
									
									 u
								
								 μ
							
							 
								 
								 
									 
									 2
									 π
								
								 
									 
										 
										 a
										 ρ
									
								
							
						
					
				
			
			 
		
		 
			 
				 
					 
						 
						 
							 
								 y
							
							 
								 
									 
									 
										 
											 
											 u
											 B
										
									
									 
										 
											 
											 a
										
									
								
							
						
						 
							 
								 
								 a
								 ρ
							
							 ρ
						
					
					 
						 0
					
				
			
			 
		
		 
			 
				 
					 
						 
						 
							 
								 z
							
							 
								 
									 
									 
										 
											 
											 u
											 B
										
									
									 
										 a
									
								
							
						
						 
							 a
							 0
						
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 a
										
										 u
									
									 μ
								
								 
									 
									 
										 
										 2
										 π
									
									 ρ
								
							
						
					
				
			
			 
		
		 
			 
		
		 
			 
				 Cálculo através do Enlace:
			
		
		 
			 
				 Cálculo do enlace λ(ρ)
			
		
		 
			 
				 
					 
						 λ
						 
							 ρ
						
					
					 
						 
							 
							 
								 
									 z
								
								 
									 
									 
										 
											 y
										
										 
											 
												 
												 B
												 
													 a
												
											
										
									
									 
										 ρ
										 
											 
											 ρ
											 a
										
									
								
							
							 
								 0
								 a
							
						
						 
							 simplify
						
						 
							 
								 assume
								 
									 
									 a
									 real
								
							
						
						 
							 
								 assume
								 
									 
									 ρ
									 real
								
							
						
						 
							 
								 assume
								 
									 
									 a
									 0
								
							
						
						 
							 
								 assume
								 
									 
									 ρ
									 0
								
							
						
						 
							 
								 
								 
									 
									 
										 
										 
											 
											 
												 
												 I
												 a
											
											 μ
										
										 
											 
												 
												 
													 ln
													 
														 
														 a
														 ρ
													
												
												 
													 ln
													 ρ
												
											
										
									
									 
										 
										 2
										 π
									
								
							
						
					
				
			
			 
		
		 
			 
				 Cálculo de V femλ
					 :
				
			
		
		 
			 
				 
					 
						 
						 
							 
								 
								 u
								 
									 
										 
										 
											 
												 ρ
											
											 
												 
												 
													 
														 z
													
													 
														 
														 
															 
																 y
															
															 
																 
																	 
																	 B
																	 
																		 a
																	
																
															
														
														 
															 ρ
															 
																 
																 ρ
																 a
															
														
													
												
												 
													 0
													 a
												
											
										
									
								
							
						
					
					 
						 simplify
					
					 
						 
							 assume
							 
								 
								 a
								 real
							
						
					
					 
						 
							 assume
							 
								 
								 ρ
								 real
							
						
					
					 
						 
							 assume
							 
								 
								 a
								 0
							
						
					
					 
						 
							 assume
							 
								 
								 ρ
								 0
							
						
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 
												 
												 a
												 2
											
										
										 u
									
									 μ
								
								 
									 
									 
										 
										 
											 
											 2
											 π
										
										 ρ
									
									 
										 
											 
											 a
											 ρ
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 
					 V
					 
						 
							 
							 
								 
								 
									 
									 
										 
											 ρ
										
										 
											 λ
											 ρ
										
									
								
							
							 u
						
						 
							 simplify
						
						 
							 
								 
								 
									 
									 
										 
										 
											 
											 
												 
												 I
												 
													 
													 a
													 2
												
											
											 u
										
										 μ
									
									 
										 
										 
											 
											 
												 
												 2
												 π
											
											 ρ
										
										 
											 
												 
												 a
												 ρ
											
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 Aplicando diretamente o resultado de λ(ρ) obtido:
ρ
									
									 
										 
											 
											 
												 
												 
													 
													 
														 
														 
															 
															 I
															 a
														
														 μ
													
													 
														 
															 
															 
																 ln
																 
																	 
																	 a
																	 ρ
																
															
															 
																 ln
																 ρ
															
														
													
												
												 
													 
													 2
													 π
												
											
										
									
								
							
						
						 u
					
					 
						 simplify
					
					 
						 
							 
							 
								 
								 
									 
									 
										 
										 
											 
											 I
											 
												 
												 a
												 2
											
										
										 u
									
									 μ
								
								 
									 
									 
										 
										 
											 
											 2
											 π
										
										 ρ
									
									 
										 
											 
											 a
											 ρ
										
									
								
							
						
					
				
			
			 
		
		 
			 
				 Como era de se esperar por todos os métodos utilizados encontramos o mesmo valor para V fem
					 .
				
			
		
	
	 
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