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Suppose you have a long solid non-conducting cylinder of length L and radius R1 where the cylinder is long enough to treat as an infinitely long one in terms of calculating the electric field. The charge density is p Coaxial to this cylinder is a conducting cylindrical shell of the TRL same length and inner radius R2. The charge density on the inner surface is o = The 2nR2L total charge on the solid cylinder is Q and on the inner surface of the conducting cylinder is -Q, why must this be the case? Note there is no charge on the outer surface of the cylindrical shell and the outer radius is R3 which is only a little larger than R2. A) Determine the electric field as a function of r in the regions; 0

Suppose you have a long solid non-conducting cylinder of length L and radius R1 where the cylinder is long enough to treat as an infinitely long one in terms of calculating the electric field. The charge density is p Coaxial to this cylinder is a conducting cylindrical shell of the TRL same length and inner radius R2. The charge density on the inner surface is o = The 2nR2L total charge on the solid cylinder is Q and on the inner surface of the conducting cylinder is -Q, why must this be the case? Note there is no charge on the outer surface of the cylindrical shell and the outer radius is R3 which is only a little larger than R2. A) Determine the electric field as a function of r in the regions; 0

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R2 <r< R3 r> R3 B) Determine the potential as a function of r in the same regions C) What is the potential difference between R1 and R2 ? D) Using the result from part C what is the capacitance (note the charge is Q)? This is not realistic as you must have two conductors as the positive and negative sides of a capacitor, but it's a good exercise in calculating field, potential and capacitance. R3 R2 R1 This is not meant to be to scale. Just to show the arrangement OFo
Transcribed Image Text:R2 <r< R3 r> R3 B) Determine the potential as a function of r in the same regions C) What is the potential difference between R1 and R2 ? D) Using the result from part C what is the capacitance (note the charge is Q)? This is not realistic as you must have two conductors as the positive and negative sides of a capacitor, but it's a good exercise in calculating field, potential and capacitance. R3 R2 R1 This is not meant to be to scale. Just to show the arrangement OFo
Suppose you have a long solid non-conducting cylinder of length L and radius R1 where the cylinder is long enough to treat as an infinitely long one in terms of calculating the electric field. The charge density is p Coaxial to this cylinder is a conducting cylindrical shell of the %3D -Q same length and inner radius R2. The charge density on the inner surface is o The 2nR2L total charge on the solid cylinder is Q and on the inner surface of the conducting cylinder is -Q, why must this be the case? Note there is no charge on the outer surface of the cylindrical shell and the outer radius is R3 which is only a little larger than R2. A) Determine the electric field as a function of r in the regions; 0<r< R1 R1 <r< R2 R2 <r< R3 r> R3 B) Determine the potential as a function of r in the same regions C) What is the potential difference between R1 and R2 ? D) Using the result from part C what is the capacitance (note the charge is Q)? This is not realistic as you must have two conductors as the positive and negative sides of a capacitor, but it's a good exercise in calculating field, potential and capacitance. D,Focus
Transcribed Image Text:Suppose you have a long solid non-conducting cylinder of length L and radius R1 where the cylinder is long enough to treat as an infinitely long one in terms of calculating the electric field. The charge density is p Coaxial to this cylinder is a conducting cylindrical shell of the %3D -Q same length and inner radius R2. The charge density on the inner surface is o The 2nR2L total charge on the solid cylinder is Q and on the inner surface of the conducting cylinder is -Q, why must this be the case? Note there is no charge on the outer surface of the cylindrical shell and the outer radius is R3 which is only a little larger than R2. A) Determine the electric field as a function of r in the regions; 0<r< R1 R1 <r< R2 R2 <r< R3 r> R3 B) Determine the potential as a function of r in the same regions C) What is the potential difference between R1 and R2 ? D) Using the result from part C what is the capacitance (note the charge is Q)? This is not realistic as you must have two conductors as the positive and negative sides of a capacitor, but it's a good exercise in calculating field, potential and capacitance. D,Focus
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