A very long insulating cylinder of charge of radius 2.60 cm carries a uniform linear density of 15.0 nC/m . Part A If you put one probe of a

Question

A very long insulating cylinder of charge of radius 2.60 cm carries a uniform linear density of 15.0 nC/m . Part A If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 200 V

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Khoii Minh 4 years 2021-08-24T20:31:24+00:00 1 Answers 50 views 0

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  1. Adela
    0
    2021-08-24T20:32:34+00:00
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    Given Information:  

    Radius = ra = 2.60 cm = 0.026 m

    Density = J = 15.0 nC/m

    change in potential difference = ΔV = 200 V

    Required Information:  

    Distance = d = ?

    Answer:

    distance = 0.088 m

    Explanation:

    As we know

    ΔV = Vb – Va = J/4πε₀*ln(rb/ra)

    Where ra and rb is the point where potential difference is Va and Vb respectively

    1/4πε₀ = 9×10⁹ N.m²/C²

    We want to find the distance d = rb – ra

    ΔV = J/4πε₀*ln(rb/ra)

    200 = 9×10⁹*15×10⁻⁹*ln(rb/ra)

    200/135 = ln(rb/ra)

    1.48 = ln(rb/ra)

    taking e on both sides yields

    e^(1.48) = rb/ra

    4.39 = rb/ra

    rb = 4.39*0.026

    rb = 0.114 m

    Therefore, the required distance is

    d = rb – ra

    d = 0.114 – 0.026

    d = 0.088 m

    Therefore, the other probe must be placed 0.088 m from the surface so that the voltmeter reads 200 V

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