4.1 A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

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Payal Gupta | Contributor-Level 10

5 months ago

4.1 Number of turns of the circular coil, n = 100

Radius of each turn, r = 8.0 cm = 0.08 m

Current flowing in the coil, I = 0.4 A

Magnitude of the magnetic field at the centre of the coil is given as

$|\overset{?}{B}|$ = $\frac{μ_{0}}{4 π} \frac{2 π n I}{r}$ where $μ_{0}$ = Permeability of free space = 4 $π \times 10^{- 7}$ Tm $A^{- 1}$
Hence, $|\overset{?}{B}|$ = $\frac{4 π \times 10^{- 7}}{4 π} \frac{2 π \times 100 \times 0.4}{0.08}$ = 3.14 $\times 10^{- 4}$ T

4.1 Number of turns of the circular coil, n = 100Radius of each turn, r = 8.0 cm = 0.08 mCurrent flowing in the coil, I = 0.4 AMagnitude of the magnetic field at the centre of the coil is given as <math> <mfenced open="|" close="|" separators="|"> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> </mfenced> </math> = <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>4</mn> <mi>π</mi> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> <mi>n</mi> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> </math> where <math> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> = Permeability of free space = 4 <math> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> </math> Tm <math> <msup> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> Hence, <math> <mfenced open="|" close="|" separators="|"> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> </mfenced> </math> = <math> <mfrac> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> <mi mathvariant="normal"> </mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> <mo>×</mo> <mn>100</mn> <mo>×</mo> <mn>0.4</mn> </mrow> </mrow> <mrow> <mrow> <mn>0.08</mn> </mrow> </mrow> </mfrac> </math> = 3.14 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </math> T

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4.1 A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

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