4.3 A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

7 Views | Posted 5 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

5 months ago

4.3 Current in the wire, I = 50 A

The distance of the point from the wire, r = 2.5 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, $|\overset{?}{B}|$ = $\frac{4 π \times 10^{- 7}}{4 π} \frac{2 \times 50}{2.5}$ = 4.0 $\times 10^{- 6}$ T

The direction of the current in the wire is vertically downward. Hence, according to Maxwell’s right hand rule, the direction of the magnetic field at the given point is vertically upward.

4.3 Current in the wire, I = 50 AThe distance of the point from the wire, r = 2.5 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>50</mn> </mrow> </mrow> <mrow> <mrow> <mn>2.5</mn> </mrow> </mrow> </mfrac> </math> = 4.0 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mrow> </msup> </math> TThe direction of the current in the wire is vertically downward. Hence, according to Maxwell’s right hand rule, the direction of the magnetic field at the given point is vertically upward.

0 Upvotes 0 Downvotes

4.3 A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question