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. `2 B _(0) L ^(2) Wb`
B. `3 B _(0) L ^(2) Wb`
C. `4B _(0)L ^(2) Wb`
D. `sqrt29 B _(0) L ^(2) Wb`

Answer

C

Explanation

Magnetic flux is defined as the total number of magnetic lines of force passing normally through an area placed in a magnetic field and is equal to the magnetic flux linked with that area.
Square lies in X-Y plane in `vecB so vecA= L ^(2) hatk`
`Q = B.A`
`- B _(0) (2 hati + 3 hatj + 4 hatk) . ( L ^(2) hatk )`
`= B _(0) [ 2 xx hati hatk + 3 xx hatj hatk + 4 xx hatk.hatk]`
`= B _(0) L ^(2) [0+ 0+ 4]`
`= 4 B _(0) L ^(2) Wb.`