5.12 A short bar magnet has a magnetic moment of 0.48 J T^–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

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Payal Gupta | Contributor-Level 10

4 months ago

5.12 Magnetic moment of the bar magnet, M = 0.48 J/T

The distance, d = 10 cm = 0.1 m

The magnetic field at a distance d from the centre of the magnet on the axis is given by the relation:

B = $\frac{μ_{0}}{4 π} \frac{2 M}{d^{3}}$ , where $μ_{0}$ = Permeability of free space = 4 $π \times 10^{- 7}$ T m $A^{- 1}$ $π \times 10^{- 7}$

B = $\frac{4 π \times 10^{- 7} \times 2 \times 0.48}{4 π \times {0.1}^{3}}$ = 0.96 $\times 10^{- 6}$ T = 0.96 G

The magnetic field is along S – N direction.

The distance, d = 10 cm = 0.1 m

The magnetic field at a distance d from the centre of the magnet on the equatorial line of the magnet is given by the relation:

B = $\frac{μ_{0}}{4 π} \frac{M}{d^{3}}$ , where $μ_{0}$ = Permeability of free space = 4 $π \times 10^{- 7}$ T m $A^{- 1}$

B = $\frac{4 π \times 10^{- 7} \times 0.48}{4 π \times {0.1}^{3}}$ = 0.48 T = 0.48 $\times 10^{- 6}$ G

The magnetic field is along N – S direction.

5.12 Magnetic moment of the bar magnet, M = 0.48 J/TThe distance, d = 10 cm = 0.1 mThe magnetic field at a distance d from the centre of the magnet on the axis is given by the relation:B = <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>M</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </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> T m <math> <msup> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> <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> B = <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> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>0.48</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>0.1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> = 0.96 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mrow> </msup> </math> T = 0.96 GThe magnetic field is along S – N direction.The distance, d = 10 cm = 0.1 mThe magnetic field at a distance d from the centre of the magnet on the equatorial line of the magnet is given by the relation:B = <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> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </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> T m <math> <msup> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> B = <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> <mo>×</mo> <mn>0.48</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>0.1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> = 0.48 T = 0.48 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mrow> </msup> </math> GThe magnetic field is along N – S direction.

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5.12 A short bar magnet has a magnetic moment of 0.48 J T^–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

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5.12 A short bar magnet has a magnetic moment of 0.48 J T–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

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5.12 A short bar magnet has a magnetic moment of 0.48 J T^–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.