A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 uC/m². Determin

Question

A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a
uniform charge density of 1.3 uC/m². Determine the electric flux through a spherical
surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center.
a. 5.7 N·m2/C
b. 4.9 Nm2/C
c. 6.4 Nm2/C
d. 7.2 N·m2/C
e. 15 N·m2/C​

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Lệ Thu 5 years 2021-09-05T00:55:28+00:00 1 Answers 18 views 0

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  1. Philomena
    0
    2021-09-05T00:57:19+00:00
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    Answer:

    The correct option is B

    Explanation:

    from the question we are told that

        The radius of the cylinder is r = 3.0 cm = \frac{3}{100} = 0.03 \ m

          The uniform charge density is  \eta = 1.3 \mu C/m^2 = 1.3 *10^{-6} C/m^2

          The radius of the spherical surface  r_s = 2.0 \ cm = \frac{2}{100} = 0.02 \ m

    Generally the flux through the spherical surface  is mathematically represented as

            \phi = \frac{Q}{\epsilon_o}

    Where  \epsilon_o is the permittivity of free space with a value of  \epsilon_o = 8.85*10^{-12} F/m

    Q is the quantity of charge which is mathematically represented as

            Q = \eta * V

    Where V is the volume of the sphere which is mathematically represented as

          V = \frac{4}{3} \pi r_s^3

    substituting values

          V = \frac{4}{3}* 3.142 * 0.02^3

          V = 3.351*10^{-5} \ m^3

    So

        Q = 1.3 *10^{-6} * 3.351*10^{-5}

        Q = 4.3569 *10^{-11} \ C

    So

         \phi = \frac{ 4.3569 *10^{-11}}{8.85*10^{-12}}

          \phi = 4.92 N\cdot m ^2 /C

     

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