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An infinitely long cylinder of radius R is located along the z-axis in a tube with an outer diameter of 3R so that the outside of the cylinder touches the inside of the tube. The electric fields in this system are: inside the cylinder: E₁ = A₁r²e, inside the tube: E2 = A₂r er. (a) Verify that E₁ and E2 are electric fields. (b) Calculate the charge density: (i) inside the cylinder (ii) inside the tube.

An infinitely long cylinder of radius R is located along the z-axis in a tube with an outer diameter of 3R so that the outside of the cylinder touches the inside of the tube. The electric fields in this system are: inside the cylinder: E₁ = A₁r²e, inside the tube: E2 = A₂r er. (a) Verify that E₁ and E2 are electric fields. (b) Calculate the charge density: (i) inside the cylinder (ii) inside the tube.

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An infinitely long cylinder of radius R is located along the z-axis in a tube with an outer diameter of 3R so that the outside of the cylinder touches the inside of the tube. The electric fields in this system are: inside the cylinder: E₁ = A₁r² er inside the tube: E2 = A2r er. (a) Verify that E₁ and E2 are electric fields. (b) Calculate the charge density: (i) inside the cylinder (ii) inside the tube.
Transcribed Image Text:An infinitely long cylinder of radius R is located along the z-axis in a tube with an outer diameter of 3R so that the outside of the cylinder touches the inside of the tube. The electric fields in this system are: inside the cylinder: E₁ = A₁r² er inside the tube: E2 = A2r er. (a) Verify that E₁ and E2 are electric fields. (b) Calculate the charge density: (i) inside the cylinder (ii) inside the tube.
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