Qstnid -Iv-3-the Magnetic Field Inside A Long Solenoid Of 50 Turns Cm-1 Is Increased From 2.5 &Times; 10-3 T To 2.5 T When An Iron Core Of Cross-sectional Area 4 Cm2 Is Inserted Into It. Find (A) The Current In The Solenoid (B) The Magnetisation I Of The Core And (C) The Pole Strength Developed In The Core. (A) The Current In The Solenoid (B) The Magnetisation I Of The Core And (C) The Pole Strength Developed In The Core. - 37: Magnetic Properties Of Matter

Home Learn Fast select Course

Show Unit/Chapter Change Unit Change Subject Last Menu

NEET-XII-Physics

37: Magnetic Properties of Matter

with Solutions - page 2

Qstn# iv-3 Prvs-Qstn Next-Qstn

#3
The magnetic field inside a long solenoid of 50 turns cm^-1 is increased from 2.5 × 10^-3 T to 2.5 T when an iron core of cross-sectional area 4 cm² is inserted into it. Find (a) the current in the solenoid (b) the magnetisation I of the core and (c) the pole strength developed in the core. (a) the current in the solenoid (b) the magnetisation I of the core and (c) the pole strength developed in the core.
Ans : Given:
Magnetic field strength without iron core, B₁ = 2.5 × 10^-3 T
Magnetic field after introducing the iron core, B₂ = 2.5 T
Area of cross-section of the iron core, A = 4 × 10^-4 m²
Number of turns per unit length, n = 50 turns/cm = 5000 turns/m (a) Magnetic field produced by a solenoid `` \left(B\right)`` is given by,
`` B={\,\mathrm{\,\mu \,}}_{0}ni``,
where i = electric current in the solenoid
2.5 × 10^-3 = 4`` \,\mathrm{\,\pi \,}`` × 10^-7× 5000 × i
`` \Rightarrow i=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}\times 5000}``
`` =0.398\,\mathrm{\,A\,}=0.4\,\mathrm{\,A\,}``
`` ``
`` \left(b\right)\,\mathrm{\,Magneti\,}\text{sa}\,\mathrm{\,tion\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}``
`` I\mathit{=}\frac{B}{{\mu }_{\mathit{0}}}\mathit{-}H,``
`` \text{w}\,\mathrm{\,here\,}B\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,net\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,field\,}\,\mathrm{\,after\,}\,\mathrm{\,introducing\,}\,\mathrm{\,the\,}\,\mathrm{\,core\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.B=2.5\,\mathrm{\,T\,}.``
`` \,\mathrm{\,And\,}{\,\mathrm{\,\mu \,}}_{0}H\,\mathrm{\,will\,}\,\mathrm{\,be\,}\,\mathrm{\,the\,}\,\mathrm{\,magnetising\,}\,\mathrm{\,field\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.\,\mathrm{\,the\,}\,\mathrm{\,diffrence\,}\,\mathrm{\,between\,}\,\mathrm{\,the\,}\,\mathrm{\,two\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,fields\,}\text{'}\,\mathrm{\,strengths\,}.``
`` \Rightarrow I=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}.\left({B}_{2}-{B}_{1}\right)``
`` \Rightarrow I=\frac{2.5\left(1-{\displaystyle \frac{1}{1000}}\right)}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}``
`` \Rightarrow I\approx 2\times {10}^{6}\,\mathrm{\,A\,}/\,\mathrm{\,m\,}``
`` \left(\,\mathrm{\,c\,}\right)\,\mathrm{\,Intensity\,}\,\mathrm{\,of\,}\,\mathrm{\,magneti\,}\text{s}\,\mathrm{\,ation\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,},``
`` I\mathit{=}\frac{M}{V}``
`` \mathit{\Rightarrow }I\mathit{=}\frac{m\times 2I}{A\times 2I}\mathit{=}\frac{m}{A}``
`` \mathit{\Rightarrow }m\mathit{=}lA``
`` \Rightarrow ``m= 2 × 10⁶ × 4 × 10^-4
`` \Rightarrow ``m= 800 A-m
Page No 286: (a) Magnetic field produced by a solenoid `` \left(B\right)`` is given by,
`` B={\,\mathrm{\,\mu \,}}_{0}ni``,
where i = electric current in the solenoid
2.5 × 10^-3 = 4`` \,\mathrm{\,\pi \,}`` × 10^-7× 5000 × i
`` \Rightarrow i=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}\times 5000}``
`` =0.398\,\mathrm{\,A\,}=0.4\,\mathrm{\,A\,}``
`` ``
`` \left(b\right)\,\mathrm{\,Magneti\,}\text{sa}\,\mathrm{\,tion\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}``
`` I\mathit{=}\frac{B}{{\mu }_{\mathit{0}}}\mathit{-}H,``
`` \text{w}\,\mathrm{\,here\,}B\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,net\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,field\,}\,\mathrm{\,after\,}\,\mathrm{\,introducing\,}\,\mathrm{\,the\,}\,\mathrm{\,core\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.B=2.5\,\mathrm{\,T\,}.``
`` \,\mathrm{\,And\,}{\,\mathrm{\,\mu \,}}_{0}H\,\mathrm{\,will\,}\,\mathrm{\,be\,}\,\mathrm{\,the\,}\,\mathrm{\,magnetising\,}\,\mathrm{\,field\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.\,\mathrm{\,the\,}\,\mathrm{\,diffrence\,}\,\mathrm{\,between\,}\,\mathrm{\,the\,}\,\mathrm{\,two\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,fields\,}\text{'}\,\mathrm{\,strengths\,}.``
`` \Rightarrow I=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}.\left({B}_{2}-{B}_{1}\right)``
`` \Rightarrow I=\frac{2.5\left(1-{\displaystyle \frac{1}{1000}}\right)}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}``
`` \Rightarrow I\approx 2\times {10}^{6}\,\mathrm{\,A\,}/\,\mathrm{\,m\,}``
`` \left(\,\mathrm{\,c\,}\right)\,\mathrm{\,Intensity\,}\,\mathrm{\,of\,}\,\mathrm{\,magneti\,}\text{s}\,\mathrm{\,ation\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,},``
`` I\mathit{=}\frac{M}{V}``
`` \mathit{\Rightarrow }I\mathit{=}\frac{m\times 2I}{A\times 2I}\mathit{=}\frac{m}{A}``
`` \mathit{\Rightarrow }m\mathit{=}lA``
`` \Rightarrow ``m= 2 × 10⁶ × 4 × 10^-4
`` \Rightarrow ``m= 800 A-m
Page No 286:

#3-a
the current in the solenoid (b) the magnetisation I of the core and (c) the pole strength developed in the core.
Ans : Magnetic field produced by a solenoid `` \left(B\right)`` is given by,
`` B={\,\mathrm{\,\mu \,}}_{0}ni``,
where i = electric current in the solenoid
2.5 × 10^-3 = 4`` \,\mathrm{\,\pi \,}`` × 10^-7× 5000 × i
`` \Rightarrow i=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}\times 5000}``
`` =0.398\,\mathrm{\,A\,}=0.4\,\mathrm{\,A\,}``
`` ``
`` \left(b\right)\,\mathrm{\,Magneti\,}\text{sa}\,\mathrm{\,tion\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}``
`` I\mathit{=}\frac{B}{{\mu }_{\mathit{0}}}\mathit{-}H,``
`` \text{w}\,\mathrm{\,here\,}B\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,net\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,field\,}\,\mathrm{\,after\,}\,\mathrm{\,introducing\,}\,\mathrm{\,the\,}\,\mathrm{\,core\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.B=2.5\,\mathrm{\,T\,}.``
`` \,\mathrm{\,And\,}{\,\mathrm{\,\mu \,}}_{0}H\,\mathrm{\,will\,}\,\mathrm{\,be\,}\,\mathrm{\,the\,}\,\mathrm{\,magnetising\,}\,\mathrm{\,field\,},\,\mathrm{\,i\,}.\,\mathrm{\,e\,}.\,\mathrm{\,the\,}\,\mathrm{\,diffrence\,}\,\mathrm{\,between\,}\,\mathrm{\,the\,}\,\mathrm{\,two\,}\,\mathrm{\,magnetic\,}\,\mathrm{\,fields\,}\text{'}\,\mathrm{\,strengths\,}.``
`` \Rightarrow I=\frac{2.5\times {10}^{-3}}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}.\left({B}_{2}-{B}_{1}\right)``
`` \Rightarrow I=\frac{2.5\left(1-{\displaystyle \frac{1}{1000}}\right)}{4\,\mathrm{\,\pi \,}\times {10}^{-7}}``
`` \Rightarrow I\approx 2\times {10}^{6}\,\mathrm{\,A\,}/\,\mathrm{\,m\,}``
`` \left(\,\mathrm{\,c\,}\right)\,\mathrm{\,Intensity\,}\,\mathrm{\,of\,}\,\mathrm{\,magneti\,}\text{s}\,\mathrm{\,ation\,}\left(I\right)\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,},``
`` I\mathit{=}\frac{M}{V}``
`` \mathit{\Rightarrow }I\mathit{=}\frac{m\times 2I}{A\times 2I}\mathit{=}\frac{m}{A}``
`` \mathit{\Rightarrow }m\mathit{=}lA``
`` \Rightarrow ``m= 2 × 10⁶ × 4 × 10^-4
`` \Rightarrow ``m= 800 A-m
Page No 286: