Question:

If $\theta_1$ and $\theta_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by :

Updated On: May 4, 2024
  • $\tan^2 \theta = \tan^2 \theta_1 + \tan^2 \theta_2$
  • $\cot^2 \theta = \cot^2 \theta_1 - \cot^2 \theta_2$
  • $\tan^2 \theta = \tan^2 \theta_1 - \tan^2 \theta_2$
  • $\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2$
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The Correct Option is D

Solution and Explanation

$\tan \theta_1 = \frac{\tan \theta}{ \cos \alpha}$ $\Rightarrow \tan \theta_2 =\frac{\tan \theta }{\cos (90 - \alpha )}= \frac{\tan \theta}{\sin \alpha}$ $\Rightarrow \sin^2 \alpha + \cos^2 \alpha = 1 $ $\Rightarrow \cot^2 \theta_2 + \cot^2 \theta_1 = \cot^2 \theta$
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Concepts Used:

Magnetism & Matter

Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.

Magnetite is the world’s first magnet. This is also called a natural magnet.  Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.

Read More: Magnetism and Matter

Some of the properties of the magnetic field lines are:

  • The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
  • They form closed loops traversing inside the magnet. 
  • But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
  • More number of close lines indicate a stronger magnetic field
  • The lines do not intersect each other
  • The tangent drawn at the field line gives the direction of the field at that point.