Magnetic Effects & Magnetism

JEE Main level, numerical answer, medium

252 of 276

Question 252 of 276

A long solenoid with 1000turnsm−11000turns{m}^{-1} has a core material with relative permeability 500500 and volume 103cm3.{10}^{3}{cm}^{3}. If the core material is replaced by another material having relative permeability of 750750 with same volume maintaining same current of 0.75A0.75A in the solenoid, the fractional change in the magnetic moment of the core would be approximately (x499).\left(\dfrac{x}{499}\right). Find the value of x.x.

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Answer: 250

M⃗=magneticmoment(m⃗)V\vec{M}=\dfrac{magneticmoment\left(\vec{m}\right)}{V}
⇒χH⃗=m⃗V\Rightarrow \chi \vec{H}=\dfrac{\vec{m}}{V}
⇒m⃗=(μr−1)NiV\Rightarrow \vec{m}=\left({\mu }_{r}-1\right)NiV
∴Δmm=[(750−1)−(500−1)]NiV(500−1)NiV=250∴\dfrac{\Delta m}{m}=\dfrac{[\left(750-1\right)-\left(500-1\right)]NiV}{\left(500-1\right)NiV}=250

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