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

The area of the coil is given by `vec(A) = L^(2)hat(k)` as the square lies in the xy plane, area vector is directed along the Z-axis.
Flux `phi = vec(B) cdot vec(A) = B_(0)(2 hat(i)+3hat(j)+4hat(k))cdot L^(3)hat(k)`
`( :' k cdot k = 1 and hat(i) cdot hat(k) = hat(j) cdot hat(k)=0)`
`phi = B_(0)L^(2) cdot 4 = 4 B_(0)L^(2)Wb` [Option (c)]