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?

3 Views | Posted 4 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

4 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

0 Upvotes 0 Downvotes

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