A 10.0-cm diameter hemisphere lies within a uniform electric field of magnitude 1000NC and direction perpendicular to the flat side of the h

Question

A 10.0-cm diameter hemisphere lies within a uniform electric field of magnitude 1000NC and direction perpendicular to the flat side of the hemisphere. The hemisphere contains no charge, and the flux through the base is in the outward direction. The flux through the rounded portion of the surface is

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Mộc Miên 3 years 2021-08-30T13:54:51+00:00 1 Answers 5 views 0

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  1. minhkhang
    1
    2021-08-30T13:56:34+00:00
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    Answer:

    Φcurved= 7.86 Nm²/C

    Φbase= -7.86 Nm²/C

    Explanation:

    Given that

    diameter of the hemisphere is 10cm

    Radius =diamter/2

    Radius = 10/2 =5cm =0.05m

    Electric field =1000N/C.

    1. Flux=? At the base

    Let choose a coordinate system where the origin is at the center of the base, such that the base is in the xy plane

    Flux is given as

    Φ=E×A

    The area of the base hemisphere is a circle and it is given as πr²

    Then,

    Φ=- πr²E k

    Φ=- 3.142×0.05²×1000 k

    Φ=-7.86 k Nm²/C

    It is in the negative direction of the z half space plane

    2. Flux=? At the curved surface

    The flux the base is equal to negative of the flux at the curved since the entire flux in the enclosed system is zero

    Therefore

    Φbase + Φcurved= 0

    Φcurved=-Φbase

    Then,

    Φcurved= -(-7.86 k Nm²/C)

    Φcurved= 7.86 k Nm²/C

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