Lesson 7 of 12 · 6 min
The solenoid
NCERT §4.7
The coil Kabir's electrons circle in is a solenoid: 500 turns wound evenly along 50 cm, carrying 0.8 A. Why is the field inside so even, and where did the 1 mT come from?
The lesson in notes
In short
A solenoid is a long insulated wire wound as a closely spaced helix; a long solenoid is one whose length is much more than its radius. Each turn acts as a circular loop.
Between neighbouring turns the fields cancel. Inside, the field is strong, uniform and along the axis; just outside it is weak, and for a very long solenoid it is taken as zero.
A rectangular Amperian loop with one side h inside along the axis and one outside gives Bh = μ₀(nh)I, so B = μ₀nI, with n counting the turns in each metre of winding.
The inside field does not depend on the radius or on the position inside, only on n and I. Its direction follows the right-hand rule.
A solenoid is the usual way to make a uniform field; a soft iron core inside makes it much larger.
Example 4.8: 500 turns on 0.5 m (n = 1000 per metre) with 5 A: B = 4π × 10⁻⁷ × 10³ × 5 = 6.28 × 10⁻³ T. The ratio of length to radius is 50, so the long-solenoid formula is fair.