4.2 A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

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Payal Gupta | Contributor-Level 10

5 months ago

4.2 Current in the wire, I = 35 A

Distance of a point from the wire, r = 20 cm = 0.2 m

Magnitude of the magnetic field at this point is given as

$|\overset{?}{B}|$ = $\frac{μ_{0}}{4 π} \frac{2 I}{r}$ where $μ_{0}$ = Permeability of free space = 4 $π \times 10^{- 7}$ Tm $A^{- 1}$

Hence, $|\overset{?}{B}|$ = $\frac{4 π \times 10^{- 7}}{4 π} \frac{2 \times 35}{0.2}$ = 3.50 $\times 10^{- 5}$ T

4.2 Current in the wire, I = 35 ADistance of a point from the wire, r = 20 cm = 0.2 mMagnitude of the magnetic field at this point 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>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> <mo>×</mo> <mn>35</mn> </mrow> </mrow> <mrow> <mrow> <mn>0.2</mn> </mrow> </mrow> </mfrac> </math> = 3.50 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> </math> T

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4.2 A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

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