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COMEDK2023Morning ShiftPhysicsMagnetic Properties of MatterActual

If ₁ and ₂ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip is given by

Options

  1. A^2 = ^2 ₁+ ^2 ₂
  2. B^2 = ^2 ₁- ^2 ₂
  3. C^2 = ^2 ₁- ^2 ₂
  4. D^2 = ^2 ₁+ ^2 ₂

Correct answer

A. ^2 = ^2 ₁+ ^2 ₂

Step-by-step solution

Let B be the total intensity of the Earth's magnetic field, B_H be the horizontal component, and B_V be the vertical component. The true angle of dip is given by = B_V B_H . Consider two vertical planes at right angles to each other. Let the horizontal component B_H make an angle with the first plane. Then the horizontal components in the two planes are B_H and B_H . The apparent angles of dip ₁ and ₂ in these two planes are given by ₁ = B_V B_H and ₂ = B_V B_H . Taking the reciprocals, we have ₁ = B_H B_V = 1 and

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