A charge of uniform density (0.74 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potenti

Question

A charge of uniform density (0.74 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 23 cm, on the x axis? Hint: Use Calculus to solve this problem.

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Thu Cúc 5 years 2021-08-10T14:44:59+00:00 1 Answers 33 views 0

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  1. Amity
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    2021-08-10T14:46:58+00:00
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    Answer:

     V = – 3.85 V

    Explanation:

    The electric potential of a continuous charge distribution is

           V = k ∫ dq / r

    to find charge differential let’s use the concept of linear density

            λ = dq / dx

           dq = λ dx

    the distance from a load element to the point of interest

           x₀ = 23 cm = 0.23 m

           r = √ (x-x₀)² = x – x₀

    we substitute

            v = k ∫ λ dx / (x-x₀)

    we integrate and evaluate between x = 0 and x = l = 0.10 cm

           V = k λ [ln (x-x₀) – ln (-x₀)]

           

            V = k λ ln ((x-x₀) / x₀)

    let’s calculate

             V = 9 10⁹  0.74 10⁻⁹ ln ((0.23 – 0.10) / 0.23)

              V = – 3.85 V

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