Question 6 of 9beginner🔧 ApplyNumerical2 marks

A closely wound solenoid of 800 turns and area of cross section 2.5×102.5 \times 10–4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

Correct Answer

A solenoid acts like a bar magnet because both have similar magnetic field lines. The field lines remain continuous, emerging from one face and entering into the other face in both cases. A compass needle shows similar deflections near both a bar magnet and a current-carrying solenoid.

Given: N = 800 turns, A = 2.5×102.5 \times 10–4 m², I = 3.0 A

Formula: Magnetic moment m = N × I × A

Calculation: m = 800×3.0800 \times 3.0 × 2.5×102.5 \times 10–4 m = 6000×106000 \times 10–4 m = 0.6 J T–1

The associated magnetic moment is 0.6 J T–1.

Exercise: EXERCISES | Q: 5.3 | (Page 152)
For More Understanding

Explanation

From Chapter 5 'Magnetism and Matter', the textbook establishes that a bar magnet and a solenoid produce similar magnetic fields. The magnetic moment of a bar magnet equals the magnetic moment of an equivalent solenoid. The formula m = NIA is used where N is number of turns, I is current, and A is cross-sectional area.

Solution Steps

  1. Step 1: Identify given values - N = 800 turns, A = 2.5×102.5 \times 10–4 m², I = 3.0 A

  2. Step 2: Apply formula for magnetic moment: m = N × I × A

  3. Step 3: Calculate: m = 800×3.0800 \times 3.0 × 2.5×102.5 \times 10–4 = 6000×106000 \times 10–4 = 0.6 J T–1

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