Part A In terms of \sigma and \(R\), what is the charge per unit length \(\lambda\) for the cylinder? Express your answer in terms of the variables \(\sigma\), \(R\).
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Step 1: The charge per unit length λ is equal to the surface charge density σ multiplied by the area of the cylinder per unit length. Show more…
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An infinitely long cylindrical conductor has radius $R$ and uniform surface charge density $\sigma .$ (a) In terms of $\sigma$ and $R,$ what is the charge per unit length $\lambda$ for the cylinder? (b) In terms of $\sigma,$ what is the magnitude of the electric field produced by the charged cylinder at a distance $r>R$ from its axis? (c) Express the result of part (b) in terms of $\lambda$ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6$($ Section 22.4$) .$
22.29. An infinitely long cylindrical conductor has radius $R$ and uniform surface charge density $\sigma$ . (a) In terms of $\sigma$ and $R$ , what is the charge per unit length $\lambda$ for the cylinder? (b) In terms of $\sigma$ , what is the magnitude of the electric field produced by the charged cylinder at a distance $r>R$ from its axis? (c) Express the result of part (b) in terms of $\lambda$ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section $22.4 ) .$
An infinitely long cylindrical conductor has radius $R$ and uniform surface charge density $\sigma$. (a) In terms of $\sigma$ and $R$, what is the charge per unit length $\lambda$ for the cylinder? (b) In terms of s, what is the magnitude of the electric field produced by the charged cylinder at a distance $r > R$ from its axis? (c) Express the result of part (b) in terms of $\lambda$ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).
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