Which of the following relations is incorrect | vedclass

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(B) The magnetic field $B$ inside a magnetic material is given by $B = \mu_0(H + I)$.Here,$I$ is the intensity of magnetization and $H$ is the magneti

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only $b$

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(B) The magnetic field $B$ inside a magnetic material is given by $B = \mu_0(H + I)$.Here,$I$ is the intensity of magnetization and $H$ is the magnetizing field.The magnetic susceptibility $\chi_m$ is defined as the ratio of intensity of magnetization to the magnetizing field,i.e.,$\chi_m = I / H$,which implies $I = \chi_m H$.Substituting $I = \chi_m H$ into the first equation,we get $B = \mu_0(H + \chi_m H) = \mu_0 H(1 + \chi_m)$.Since $B = \mu H = \mu_0 \mu_r H$,we have $\mu_r = 1 + \chi_m$.Comparing these,option $(b)$ states $B = \mu_0(H + \chi_m)$,which is dimensionally and physically incorrect because $\chi_m$ is a dimensionless quantity and cannot be added directly to $H$ (which has units of $A/m$). Therefore,only $(b)$ is incorrect.

Which of the following relations is incorrect?
$(a) \ B = \mu_0(H + I)$
$(b) \ B = \mu_0(H + \chi_m)$
$(c) \ \mu_r = 1 + \chi_m$
$(d) \ \chi_m = I / H$
(Here,$I =$ intensity of magnetization and $H =$ magnetising field)

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Which of the following relations is incorrect?$(a) \ B = \mu_0(H + I)$$(b) \ B = \mu_0(H + \chi_m)$$(c) \ \mu_r = 1 + \chi_m$$(d) \ \chi_m = I / H$(Here,$I =$ intensity of magnetization and $H =$ magnetising field)