A uniform magnetic field exists in the space `vecB=B_(1)hati+B_(2)hatj+B_(3)hatk`. Find the magnetic flux through an area `vecS` if the area `vecS` is in (i) x-y plane (ii) y-z plane (iii) z-x plane

Explanation

(i) Since the field is uniform, we can use formula `phi_(B)=vecB,vecS`
Now when area `vecS` is in x-y plane, it means `vecS=Sveck`
Hence `phi_(B)=(B_(1)hati+B_(2)hatj+B_(3)hatk).(S hatk)=-B_(3)S`