harge of uniform density (100 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of rad

Question

harge of uniform density (100 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis. Group of answer choices

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Nem 5 months 2021-08-23T19:46:51+00:00 1 Answers 5 views 0

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    2021-08-23T19:48:18+00:00

    Answer:

    The magnitude of the electric field is 8.47 N/C

    Explanation:

    Given;

    uniform charge density, λ = 100 nC/m³

    inner radii of the cylinder, r =  1.0 mm and 3.0 mm

    distance from the symmetry axis, R = 2.0 mm

    Volume =\pi (R^2 -r^2)l\\\\Volume =\pi ((2*10^{-3})^2 -(1*10^{-3})^2)l\\\\Volume =\pi (4*10^{-6} - 1*10^{-6})l\\\\Volume = 3*10^{-6} \pi l \ m^3

    Area = 2πrl

    Area =2π(2 x 10⁻)l

    Volume = A x d

    d = Volume / Area

    d = \frac{V}{A} = \frac{3*10^{-6}*\pi*l}{4\pi *10^{-3} l} = 75 *10^{-5} \ m

    the magnitude of the electric field

    E = \frac{\lambda *d}{\epsilon_o} = \frac{100*10^{-9} *75*10^{-5}}{8.854*10^{-12}} \\\\E = 8.47 \ N/C

    Therefore, the magnitude of the electric field is 8.47 N/C

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