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17 June, 22:18

At a distance of 0.220 cm from the axis of a very long charged conducting cylinder with radius 0.100cm, the electric field is 490 N/C. What is the electric field 0.616 cm from the axis of the cylinder?

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  1. 17 June, 22:39
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    At the distance of 0.220cm from the axis.

    r = 0.220cm = 0.0022m, E = 490N/C, e0 = 8.854 x 10^-12F/m

    Linear charge density = 2*π*e0*r*E = 2 x 3.142 x 8.854x10^-12 x 0.0022 x 490 = 5.998 x 10^-11C/m

    Thus, To Calculate the Electric field at the distance r = 0.616cm from the cylinder axis, we substitute the calculated linear change density in the equation

    E = (linear charge density) / 2*π*e0*r

    Here, r = 0.616cm = 0.00616m

    E = [ (5.998 x 10^-11) / (2 x 3.142 x 8.854 x 10-12 x 0.00616) ]

    E = 175N/C

    Explanation:

    The Electric field of a charged conducting cylinder obey the Gauss Law.

    Therefore, the Electric field is given as:

    E = (linear charge density) / 4πe0r,

    Where e0 is the permittivity of free space with constant value of 8.854 x 10^-12F/m, r is the radial distance from the axis.
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