5.8 A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10^–4 m², carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.

(a) What is the magnetic moment associated with the solenoid?

(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10^–2 T is set up at an angle of 30° with the axis of the solenoid?

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Payal Gupta | Contributor-Level 10

5 months ago

5.8 (a) Number of turns, n = 2000

Area of cross-section, A = 1.6 $\times 10^{- 4}$ $m^{2}$

Current, I = 4.0 A

The magnetic moment along the axis of the solenoid is calculated as

M = nAI = 2000 $\times$ 1.6 $\times 10^{- 4} \times 4$ = 1.28 A $m^{2}$

(b) Magnetic field, B = 7.5 $\times 10^{- 2}$ T

Angle between magnetic field and the axis of the solenoid, $θ$ = 30 $°$

Torque $τ = M B \sin ? θ$

= 1.28 $\times$ 7.5 $\times 10^{- 2}$ $\times \sin ? 30 °$

= 4.8 $\times 10^{- 2}$ Nm

5.8 (a) Number of turns, n = 2000Area of cross-section, A = 1.6 <math> <mo>×</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </math> <math> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> Current, I = 4.0 AThe magnetic moment along the axis of the solenoid is calculated asM = nAI = 2000 <math> <mo>×</mo> <mi> </mi> </math> 1.6 <math> <mo>×</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> <mi> </mi> <mo>×</mo> <mn>4</mn> </math> = 1.28 A <math> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> (b) Magnetic field, B = 7.5 <math> <mo>×</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> TAngle between magnetic field and the axis of the solenoid, <math> <mi>θ</mi> </math> = 30 <math> <mo>°</mo> </math> Torque <math> <mi>τ</mi> <mo>=</mo> <mi>M</mi> <mi>B</mi> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>θ</mi> </mrow> </mrow> </math> = 1.28 <math> <mo>×</mo> <mi> </mi> </math> 7.5 <math> <mo>×</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> <math> <mo>×</mo> <mi> </mi> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mn>30</mn> <mo>°</mo> </mrow> </mrow> </math> = 4.8 <math> <mo>×</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> Nm

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