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Physics · Ch 4 — Moving Charges and Magnetism
The Solenoid
4.7
The Solenoid
The Solenoid: A Source of Uniform Magnetic Field
A solenoid is a long wire wound into a tight helix. For it to be considered "long," its length must be much greater than its radius. This geometry is crucial because it produces a highly uniform magnetic field inside, similar to how a parallel-plate capacitor produces a uniform electric field.
Why the Field Inside is Uniform and Outside is Negligible
- Structure: Each turn of the solenoid acts like a circular current loop. The net magnetic field is the vector sum of the fields from all these loops.
- Cancellation between turns: Between two neighbouring turns, the magnetic field lines from adjacent loops point in opposite directions and cancel out (see Fig. 4.15a).
- Inside the solenoid: At interior points (like point P in Fig. 4.15b), the contributions from all turns add up, giving a strong, uniform field directed along the axis.
- Outside the solenoid: At exterior points (like point Q), the field is very weak. For an ideal, infinitely long solenoid, the field outside is exactly zero. For a real long solenoid, it is negligible.
Deriving the Magnetic Field Inside Using Ampere's Circuital Law
We use Ampere's law to find the magnetic field inside a long solenoid.
- Choose an Amperian loop: Consider a rectangular loop abcd (Fig. 4.16). Side ab of length lies inside the solenoid, parallel to the axis. Side cd lies outside, where the field . Sides bc and ad are perpendicular to the axis.
- Evaluate the line integral : …
Figure 4.15(a) The magnetic field due to a section of the solenoid which has been stretched out for clarity. Only the exterior semi-circular part is shown. Notice how the circular loops between neighbouring turns tend to cancel. (b) The magnetic field of a finite solenoid.
Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.
What Figure 4.15 Shows
The figure has two panels, (a) and (b), that together explain how the magnetic field of a solenoid arises from its individual turns and how it behaves inside and outside the coil.
Panel (a) shows a short, stretched-out section of the solenoid. Five turns are represented as small circles: each circle has a ⊙ on its top half (current coming out of the page) and a ⊗ on its bottom half (current going into the page). Around each turn, magnetic field lines form closed loops. Between neighbouring turns, the field lines from adjacent loops point in opposite directions and cancel — this is why the field in the gaps is nearly zero. Two points are marked: P inside the solenoid (where the field is strong and uniform) and Q outside (where the field is weak). The field lines exit the ends of the section, showing that the net field inside points along the axis. …
Figure 4.16The magnetic field of a very long solenoid. We consider a rectangular Amperian loop abcd to determine the field.
Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.
The figure shows a very long solenoid drawn as a horizontal capsule. The top wall of the solenoid has a row of ⊙ symbols (current coming out of the page), and the bottom wall has a row of × symbols (current going into the page). Inside the solenoid, several horizontal blue arrows point to the right, representing the uniform axial magnetic field . The field is labelled 'B' at the left side, and a point P is marked inside. Outside the solenoid, above it, the field is essentially zero.
A dashed rectangular Amperian loop is overlaid:
- Side lies inside the solenoid, along the field direction (bottom edge, left to right).
- Side lies outside above the solenoid.
- The vertical sides and are transverse (perpendicular to the axis).
- The interior length between the top corners is labelled .
At the right side, a stylised open right hand shows the curl direction (the right-hand rule for the field direction).
Physical idea taught by the figure
The figure is used to apply Ampere’s circuital law to an idealised long solenoid. The key assumptions are:
- The field inside is uniform and parallel to the axis.
- The field outside is zero (for a very long solenoid). …