A thin wire, carrying a positive and uniform linear charge density 2, is bent into a...

  

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A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field of this thick quarter-circle at the center, assuming the charge density is still uniform. 0 y R X R b A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field of this thick quarter-circle at the center, assuming the charge density is still uniform. 0 y R X R b