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

Since the plane of the square is in X-Y plane, its area vector (normal to the plane) will be along Z-axis.
`therefore vec A= L^(2) hatk,m^(2)`
Given, magnetic field, `vec B =B_(0)(2 hati+ 3hat j+ 4hat k)T`
Magnetic flux passing through the square is
`phi= vec B. vec A= B_(0)(2 hati+ 3hat j+ 4hat k). L^(2) hatk= 4B_(0)L^(2)Wb`
Option (c) is correct.