First slide
Earth's Magnetism
Question

If θ1 and θ2be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

Difficult
Solution

Let BH and  BV  be the horizonal and vertical components of earth's magnetic field β. Since θ is the angle of dip

tanθ=BVBH  or  cotθ=BHBV (i

Suppose planes 1 and 2 are two mutually perpendicular planes and respectively make angles θ and 90°-θ with the magnetic meridian. The vertical components of earth's magnetic field remain same in the two planes but the effective horizontal components in the planes will be

 

B1=BHcosθ  and B2=BHsinθ  The angles of dipθ1 and θ2 in the two planes are given by tanθ1=BVB1tanθ1=BVBHcosθ or cotθ1=BHcosθBV                              . . . (ii) Similarly, cotθ2=BHsinθBV                                     . . . .(iii)  From eqns. (ii) and (iii)  cot2θ1+cot2θ2=BH2BV2cos2θ+sin2θ=BH2BV2 cot2θ1+cot2θ2=cot2θ                               [ from eqn. (i)]

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