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(a) Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and length . Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Suggestion: Use the following expression and treat the cylinder as a collection of ring charges. (Use any variable or symbol stated above along with the following as necessary: k.) E = kex (x² + a²)3/2 E = -Q î 2πk (1-(x2+x2)1/2) R²) R (b) Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the following expression to find the field it creates at the same point. (Use any variable or symbol stated above along with the following as necessary: k.) î Q d
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Transcribed Image Text:(a) Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and length . Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Suggestion: Use the following expression and treat the cylinder as a collection of ring charges. (Use any variable or symbol stated above along with the following as necessary: k.) E = kex (x² + a²)3/2 E = -Q î 2πk (1-(x2+x2)1/2) R²) R (b) Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the following expression to find the field it creates at the same point. (Use any variable or symbol stated above along with the following as necessary: k.) î Q d
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Step 1: a) Determine the electric field due to cylindrical shell:
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Step 2: b) Determine the electric field due to solid cylinder:
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