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

Options

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`

Answer

C

Explanation

`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