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An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as = Q I piR2L We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A= qenc / epsilon0 (Equation 1) E Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc = Qr2/R2 On the other hand, the Gaussian surface inside the wire is given by A= 2pirL Using Equation 1, the electric field in simplified form is E = Qr | 2piR2Lepsilon0

An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as = Q I piR2L We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A= qenc / epsilon0 (Equation 1) E Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc = Qr2/R2 On the other hand, the Gaussian surface inside the wire is given by A= 2pirL Using Equation 1, the electric field in simplified form is E = Qr | 2piR2Lepsilon0

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An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as DE dÀ= Q / piR2L We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain E A = qenc / epsilon0 (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc Qr2/R2 On the other hand, the Gaussian surface inside the wire is given by A = 2pirL Using Equation 1, the electric field in simplified form is E = Qr / 2piR2Lepsilon0
Transcribed Image Text:An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as DE dÀ= Q / piR2L We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain E A = qenc / epsilon0 (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc Qr2/R2 On the other hand, the Gaussian surface inside the wire is given by A = 2pirL Using Equation 1, the electric field in simplified form is E = Qr / 2piR2Lepsilon0
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