A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current I(t) = I₀(I – t/T) for 0 ≤ t ≤ T and I(0) = 0 for t >T(figure). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

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Payal Gupta | Contributor-Level 10

4 months ago

This is a long answer type question as classified in NCERT Exemplar

applying ohm’s law

I=E/R=d $\emptyset / R d t$

I= dQ/dt or dQ/dt= d $\emptyset / R d t$

Q (t₁)-Q (t₂)= $\frac{1}{R}$ [ $\emptyset$ t₁- $\emptyset$ t₂]

$\emptyset$ t₁= L_{1
$\frac{μ_{0}}{2 π} \int_{x}^{L_{2} + x} \frac{d x}{x} I$} t₁

= $\frac{μ_{0} L_{1}}{2 π}$ I1in [ $\frac{L_{2} + x}{x}$ ]

This is a long answer type question as classified in NCERT Exemplarapplying ohm’s lawI=E/R=d <math> <mi>∅</mi> <mo>/</mo> <mi>R</mi> <mi>d</mi> <mi>t</mi> </math> I= dQ/dt or dQ/dt= d <math> <mi>∅</mi> <mo>/</mo> <mi>R</mi> <mi>d</mi> <mi>t</mi> </math> Q (t1)-Q (t2)= <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> </mfrac> </math> [ <math> <mi>∅</mi> </math> t1- <math> <mi>∅</mi> </math> t2] <math> <mi>∅</mi> </math> t1= L1 <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> </mfrac> <msubsup> <mo>∫</mo> <mrow> <mi>x</mi> </mrow> <mrow> <msub> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>+</mo> <mi>x</mi> </mrow> </msubsup> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> </mfrac> <mi>I</mi> </mrow> </mrow> </math> t1= <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> </mfrac> </math> I1in [ <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>+</mo> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> </mfrac> </math> ]

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A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current I(t) = I₀(I – t/T) for 0 ≤ t ≤ T and I(0) = 0 for t >T(figure). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

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A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current I(t) = I0(I – t/T) for 0 ≤ t ≤ T and I(0) = 0 for t >T(figure). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

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A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current I(t) = I₀(I – t/T) for 0 ≤ t ≤ T and I(0) = 0 for t >T(figure). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.