Question

The magnetic needle of tangent galvanometer is deflected at an angle 30 due to a magnet. The horizontal component of earth’s magnetic field $0.34\times {{10}^{-4}}T$is along the plane of the coil. The magnetic intensity is:
(A) $1.96\times {{10}^{-4}}T$
(B) $1.96\times {{10}^{-5}}T$
(C) $1.96\times {{10}^{4}}T$
(D) $1.96\times {{10}^{5}}T$

Answer 1

We know that the Earth's magnetic field, also called the geomagnetic field, which effectively extends several tens of thousands of kilometres into space, forms the Earth's magnetosphere. A paleomagnetic study of Australian red dacite and pillow basalt has estimated the magnetic field to be at least 3.5 billion years old. The intensity of the magnetic field is greatest near the magnetic poles where it is vertical. The intensity of the field is weakest near the equator where it is horizontal. The magnetic field's intensity is measured in gauss. The magnetic field has decreased in strength through recent years.

Complete step-by step answer:
We know that magnetic field strength, also called magnetic intensity or magnetic field intensity, the part of the magnetic field in a material that arises from an external current and is not intrinsic to the material itself. It is expressed as the vector H and is measured in units of amperes per metre.
We can also conclude that an angle that measures the departure of a moving object from its directed course. The angle of a deflection shot in gunnery, measured between the line of sight to the target and the line of sight to the aiming point.
From the given,
$B=0.34\times {{10}^{-4}}T$
Deflected $angle\theta =30{}^\circ$
So magnetic intensity is $B\tan 30{}^\circ$
$=0.34\times {{10}^{-4}}T\times \dfrac{1}{\sqrt{3}}$
$=1.96\times {{10}^{-5}}T$
Where, $\tan 30{}^\circ =\dfrac{1}{\sqrt{3}},\,and\,\sqrt{3}=1.73c$

Hence, the correct answer is B.

Note: For better understanding we should know that galvanometer, an instrument for measuring a small electrical current or a function of the current by deflection of a moving coil. The deflection is a mechanical rotation derived from forces resulting from the current. If the south pole of the magnet is brought towards the solenoid, the galvanometer shows deflection. Current flows in the coil of the solenoid in the clockwise direction and the galvanometer shows deflection towards the left. Therefore, the least value it can measure is 1mm which is the least count of this instrument. There is no least count to a galvanometer since it does not depict any quantity, while that of ammeter differs with different ranged devices.