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Question
Which of the following pairs has quantities of the same dimensions?
(a) Magnetic field B and magnetising field intensity H
(b) Magnetic field B and intensity of magnetisation I
(c) Magnetising field intensity H and intensity of magnetisation I
(d) Longitudinal strain and magnetic susceptibility
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Solution
(c) Magnetising field intensity H and intensity of magnetisation I
(d) Longitudinal strain and magnetic susceptibility
Dimension of Magnetic field B is given by,
F=Bqv
\[\Rightarrow B = \frac{F}{qv}\]
\[\Rightarrow\frac{\left[ {MLT}^{- 2} \right]}{\left[ AT \right]\left[ {LT}^{- 1} \right]} = \left[ {MT}^{- 2} A^{- 1} \right]\]
Dimension of magnetising field intensity H is given by,
H = \[\left[ \frac{Idl}{r^2} \right]\]
\[\Rightarrow\frac{\left[ AL \right]}{\left[ L^2 \right]} = \left[ {AL}^{- 1} \right]\]
Dimension of intensity of magnetisation I is also \[\left[ {AL}^{- 1} \right]\] as both Magnetising field intensity H and intensity of magnetisation I are measured in Am-1.
Hence, option (a) and option (b) is incorrect. Option (c) is correct.
As Longitudinal strain and magnetic susceptibility both are dimensionless quantity. Hence, option (d) is correct.
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