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Find out the flux through the curved sur...

Find out the flux through the curved surface of a hemisphere of radius R if it is placed in a uniform electric field E as shown in figure

Text Solution

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The number of electric line passing through the base of the hamisphere is the same as that of the lines passing through the hemisphere. The flux associated with the base of the hemisphere is `phi = -EpiR^2` (negative as it is the incoming flux). Hence, the same amount of flux wil be associated with curved surface, but the sigh of the flux will be positive as it is as outgoing flux. Hence,
`phi_(curve) = EpiR^2` .
.
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Knowledge Check

  • A hemisphere (radius R) is placed in electric field as shown in fig. Total outgoing flux is -

    A
    `piR^(2)E`
    B
    `2piR^(2)E`
    C
    `4piR^(2)E`
    D
    `(piR^(2)E)//2`

  • A hemispherical bowl of radius r is placed in uniform electric field E . The electric flux passing through the bowl is

    A
    `pir^(2)E`
    B
    `2pirE^(2)`
    C
    `4pir^(2)E`
    D
    `4pirE^(2)`

  • The electric flux through a hemispherical surface of radius R placed in a uniform electric field E parallel to the axis of the circular plane is

    A
    `(2piR)E`
    B
    `(piR^(2))E`
    C
    `(4/3piR^(3))E`
    D
    `(2/3piR^(3))E`

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