At a given place horizontal and vertical components of the earth's magnetic field `B_(H) and B_(V)` are along X and Y-axes, respectively, as shown in the figure. What is the total flux of the earth's magnetic field associated with an area S, if the area S is in the
(i) XY-plane
(ii) YZ-plane

Options

A. `0,B_(H)S`
B. `B_(H)S,O`
C. `1,B_(H)S`
D. `0.5,B_(H)S`

Answer

C

Explanation

The earth's magnetic field, `B=(B_(H)hati-B_(V)hatj)`
(i) Given, the area, `A=Shatk`
`phi_(XY)=B*A=(B_(H)hati-B_(V)hatj)Shatk=OF`
ltBrgt (ii) For the second use case the area S is in the Y-Z plane. So, `A=Shati`
`phi_(YZ)=(B_(H)hati-B_(V))Shati=B_(H)S`