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JEE Main 202131 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
31 August
Shift
Evening Shift
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Main 2021 · 31 August · Evening Shift · Physics · Magnetic Effects of Current

A long solenoid with 1000turns m ^ - 1 has a core material with...

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 .

Correct answer

0

Step-by-step solution

M→=magneticmoment(m→)V\overset{\to}{M} = \dfrac{magnetic moment \left(\overset{\to}{m}\right)}{V}
⇒χH→=m→V⇒ χ\overset{\to}{H} = \overset{\to}{m}V
⇒m→=(μr−1)NiV⇒ \overset{\to}{m} = \left({\mu}_{r} - 1\right)NiV
∴\Deltamm=[(750−1)−(500−1)]NiV(500−1)NiV=250∴ \dfrac{\Deltam}{m} = \dfrac{[ \left(750 - 1\right) - \left(500 - 1\right) ] NiV}{\left(500 - 1\right)NiV} = 250
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