A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (BQ: BP) is
\(\sqrt3:4\)
\(4:\sqrt3\)
\(\sqrt3:2\)
\(2:\sqrt3\)
The Correct Option is A
Solution and Explanation
The correct answer is (A) : \(\sqrt3:4\)
\(T∝\frac{1}{\sqrt{B\cosδ}}\)
\(⇒ \frac{T_1}{T_2} = \sqrt{\frac{B_2\cosδ_2}{B_1\cosδ_1}}\)
\(⇒ \frac{3s}{6s} = \sqrt{\frac{B_2}{B_1}×\frac{\frac{1}{2}}{\frac{\sqrt3}{2}}}\)
\(⇒ \frac{B_2}{B_1} = (\frac{1}{2})^2 × \sqrt3 \)
\(= \frac{\sqrt3}{4}\)
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Concepts Used:
Magnetic Properties of Materials
Magnetic Material:
Magnetic material is one that can repel or attract other materials. The process of attraction or repulsion of these materials depends on the arrangement of electrons, which is known as the magnetic moment of that material.
Diamagnetic - With regard to the susceptibility χ, a material is diamagnetic if χ is negative. These materials produce negative magnetization when they are placed in the magnetic field. When placed in a magnetic field, these diamagnetic materials are barely magnetized. Diamagnetic substances are the ones that are repelled by magnets.
Paramagnetic - In the presence of an external magnetic field, the substances that get weakly magnetized are known as paramagnetic substances. The magnetic dipoles align along the direction of the applied field, reinforcing and enhancing the magnetic field. These substances get weakly attracted to a magnet as they tend to move from a weaker magnetic field to a stronger one. The magnetization (M) of paramagnetic materials, discovered by Madam Curie, depends on the temperature (T) and the external magnetic field B.
M = C x (B/T)
Where M = Magnetization
C = Curie Constant
B = External magnetic field
T = Temperature
Ferromagnetic - The materials strongly attracted by the magnetic field are known as ferromagnetic materials.