Two short bar magnets of length $1\, cm$ each have magnetic moments $1.20 \,Am^2 $ and $1.00 \,Am^2 $ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the south. They have a common magnetic equator and are separated by a distance of $20.0\, cm$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to (Horizontal component of the earth's magnetic induction is $ 3.6 \times {10}^{-5} W b/m^2$
- $ 3.6 \times {10}^{-5} W b/m^2$
- $ 2.56 \times {10}^{-4} W b/m^2$
- $ 3.50 \times {10}^{-4} W b/m^2$
- $ 5.80 \times {10}^{-4} W b/m^2$
The Correct Option is B
Solution and Explanation
$B_{net} = \frac{ {\mu}_0}{4 \pi } \frac{(M_1+M_2)}{r^3} +B_H$
$ \, \, \, \, \, = \frac{ {10}^{-7} (1.2+1)}{(0.1)^3}+ 3.6 \times {10}^{-5}$
$ \, \, \, \, \, \, \, \, \, \, \, \, =2.56 \times {10}^{-4} Wb/m^2$
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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.