Question

A short magnetic needle is pivoted in a uniform magnetic field of induction 1T. Now, simultaneoulsy another magnetic field of induction $\sqrt 3 T$ is applied at right angles to the first field; the needle deflects through an angle $\theta $ where its value is
A. ${30^ \circ }$
B. ${45^ \circ }$
C. ${90^ \circ }$
D. ${60^ \circ }$

Answer 1

Hint: For solving these types of questions, we need to know about the angle of dip. Since the dip circle is positioned on a horizontal surface, a change in the dip needle will affect the horizontal component. Due to these fields that are applied to the needle, the magnet acquires an equilibrium state.

Formula used:
${B_1} = B\tan \theta $
where $\theta $ defines the angle through which the needle deflects.

Complete step by step solution:
We are aware that the portion of a material's magnetic field that results from an external current and is not intrinsic to the material itself is known as magnetic field strength, also known as magnetic intensity or magnetic field intensity. It is measured in amperes per metre and represented as the vector H.

We can also draw the conclusion that an angle is a measurement of how far an object is moving from its intended course. Measured between the line of sight to the target and the line of sight to the aiming point, the angle of a deflection shot in gunnery. From the given,
$B = 1T$ and ${B_1} = \sqrt 3 T$
We know that,
${B_1} = B\tan \theta $
where $\theta $ defines the angle through which the needle deflects.
Substituting the values we get
$\sqrt 3 = 1\tan \theta $
$ \therefore \theta = {60^ \circ }$

Hence, option D is the correct answer.

Note: It is important to keep in mind the following facts about the magnetic field:
- There are two different types of magnetic fields: the B-field and the H-field.
- Teslas are used to measure B-field (T). A/m units are used to express the H-field.
- The earth's magnetic field is oriented so that it extends from its magnetic north pole to its magnetic south pole. The inclined bar magnet is merely a fictitious magnet; it does not exist.