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A circular disk with radius R has a constant surface charge density, o. ) Determine the electric potential, V(z), a distance z directly above the center of the disk. From this potential, determine the magnitude of the electric field, E(z)|, a distance z directly above the center of the disk. Verify that your answer in part b) gives the correct result in the two extreme cases 1) very close to the charged disk (z << R) and 2) very far away from the disk (z >> R).

A circular disk with radius R has a constant surface charge density, o. ) Determine the electric potential, V(z), a distance z directly above the center of the disk. From this potential, determine the magnitude of the electric field, E(z)|, a distance z directly above the center of the disk. Verify that your answer in part b) gives the correct result in the two extreme cases 1) very close to the charged disk (z << R) and 2) very far away from the disk (z >> R).

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A circular disk with radius \( R \) has a constant surface charge density, \( \sigma \). a) Determine the electric potential, \( V(z) \), a distance \( z \) directly above the center of the disk. b) From this potential, determine the magnitude of the electric field, \( |\vec{E}(z)| \), a distance \( z \) directly above the center of the disk. c) Verify that your answer in part b) gives the correct result in the two extreme cases: 1) very close to the charged disk (\( z \ll R \)), and 2) very far away from the disk (\( z \gg R \)). **Diagram Explanation:** The diagram illustrates a circular disk viewed from above, with radius \( R \). A line is drawn vertically (dashed) from the center of the disk, representing the distance \( z \) directly above the disk's center to a point. The concepts above relate to calculating the electric potential and field due to a surface charge on the disk, with focus on different distances from the surface.
Transcribed Image Text:A circular disk with radius \( R \) has a constant surface charge density, \( \sigma \). a) Determine the electric potential, \( V(z) \), a distance \( z \) directly above the center of the disk. b) From this potential, determine the magnitude of the electric field, \( |\vec{E}(z)| \), a distance \( z \) directly above the center of the disk. c) Verify that your answer in part b) gives the correct result in the two extreme cases: 1) very close to the charged disk (\( z \ll R \)), and 2) very far away from the disk (\( z \gg R \)). **Diagram Explanation:** The diagram illustrates a circular disk viewed from above, with radius \( R \). A line is drawn vertically (dashed) from the center of the disk, representing the distance \( z \) directly above the disk's center to a point. The concepts above relate to calculating the electric potential and field due to a surface charge on the disk, with focus on different distances from the surface.
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