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A square of side L meters lies in the x-...

A square of side L meters lies in the x-y plane in a region, where the magnetic field is give by `B = B_(0) (2 hati + 3 hat j + 4 hatk)`T, where `B_(0)` is constant. The magnitude of flux passing through the square is

A

`2B_(0)L^(2)Wb`

B

`3B_(0)L^(2)Wb`

C

`4B_(0)L^(2)Wb`

D

`sqrt(29)B_(0)L^(2)Wb`

Text Solution

Verified by Experts

The correct Answer is:
C
`B=B_(0)(2hati+3hatj+4hatk)T`
`B_(l)=(4B_(0)hatk)T` or `B_(2)=(4B_(0))T`
=Component of B alnot area A
Area of the square, `A=L^(2)(m)^(2)`
`phi_(B)`(magnitude of magnetic flux)
`=B_(2)A=4B_(0)L^(2)(Tm^(2))=4B_(0)L^(2)Wb`
Observing `phi_(B)=BAcostheta`
`implies phi_(B)=(Bcostheta)A=`(component of B of along A) A
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Knowledge Check

  • A square of side L metre lies in the x - y plane in a region, where the magnetic field is given by vecB = B_(0) (2hati +3hatj +4hatk) T , where B_(0) , is constant. The magnitude of flux passing through the square is [Exemplar Problem]

    A
    `2B_(0)L^(2)Wb`
    B
    `3B_(0)L^(2)Wb`
    C
    `4B_(0)L^(2)Wb`
    D
    `sqrt(49)B_(0)L^(2)Wb`

  • A square of side x m lies in the x-y plane in a region, when the magntic field is given by vecB=B_(0)(3hati+4hatj+5hatk) T, where B_(0) is constant. The magnitude of flux passing through the square is

    A
    `5B_(0)x^(2)Wb`
    B
    `3B_(0)x^(3)Wb`
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  • Square of A meters in an X-Y plane is under magnetic field of B = (B_(0), 2hati+3hatj+4hatk)T . The magnitude of flux is given by? B_(0) = constant

    A
    `sqrt(29) B_(0) A^(2) ` Wb
    B
    `2 B_(0) A^(2) ` Wb
    C
    `4 B_(0) A^(2) ` Wb
    D
    `3 B_(0) A^(2) wb`

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