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At a location the horizontal and vertical components of Earth's magnetic field, B_H and B_V, point along the x and y axes respectively. Consider a flat area S. What is the magnetic flux of Earth's field through S when S lies in (a) the x-y plane, (b) the y-z plane, and (c) the z-x plane? Choose the value that gives the flux in case (c) (S in the z-x plane).

1. 0
2. B_V*S
3. B_H*S
4. (B_H + B_V)*S

Correct answer: B_V*S

Solution

Flux = B dot A, where A is along the normal of the plane. (a) x-y plane: normal along z; B has no z-component, flux = 0. (b) y-z plane: normal along x; B_H is along x, flux = B_H*S. (c) z-x plane: normal along y; B_V is along y, flux = B_V*S. The asked case (c) gives B_V*S.

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