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Question

Points $$A$$ and $$B$$ are situated perpendicular to the axis of a $$2 cm$$ long bar magnet at large distances $$X$$ and $$3X$$ from its centre on opposite sides. The ratio of the magnetic fields at $$A$$ and $$B$$ will be approximately equal to


A
1:9
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B
2:9
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C
27:1
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D
9:1
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Solution

The correct option is C $$27 : 1$$

Magnetic field at the axial of bar magnet is given by the relation as :

 $$B\,=\,\dfrac{{{\mu }_{O}}}{2\pi }\,\dfrac{M}{{{d}^{3}}}$$ 

where d is the distance

 So, 

$$B\,\propto \,\dfrac{1}{{{d}^{3}}}$$

 $$ \dfrac{{{B}_{A}}}{{{B}_{B}}}\,\,=\,\,\dfrac{{{d}_{B}}^{3}}{{{d}_{A}}^{3}} $$

 $$ \dfrac{{{B}_{A}}}{{{B}_{B}}}\,\,=\,\,\dfrac{27}{1} $$

 Hence, the ratio of magnetic field of $$A$$ and $$B$$ is $$27 : 1$$ .


Physics
NCERT
Standard XII

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