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In the previous sections, we learned magnetic field lines produced by a current-carrying circular loop.

In this section, we will observe the pattern of the magnetic field produced by a current-carrying circular coil.

Steps:
• Take rectangular cardboard which has two holes.
• Insert a circular coil having a large number of turns through the holes (normal to the cardboard plane).
• Join the ends of the coil in series with a battery, key, and rheostat (variable resistance), as shown in the below figure.
Magnetic field produced by a current-carrying circular coil
• Spray iron filings uniformly on the cardboard. (You may use a salt sprinkler to spray.)
• Plug the key
• Tap the cardboard mildly a few times.
• Observe the pattern of the iron filings that emerges on the cardboard.
Pattern of the magnetic field produced by a current-carrying circular coil

Observations:

The magnitude of the magnetic field produced by a current-carrying circular wire at its centre is:
• Directly proportional to the current passing through the circular wire.
$\begin{array}{l}B\phantom{\rule{0.147em}{0ex}}\propto \phantom{\rule{0.147em}{0ex}}I\\ \mathit{Where},\\ B\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathit{Magnitude}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{magnetic}\phantom{\rule{0.147em}{0ex}}\mathit{field}\\ I\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathit{Current}\end{array}$
• Inversely proportional to the radius of the circular wire.
$\begin{array}{l}B\phantom{\rule{0.147em}{0ex}}\propto \phantom{\rule{0.147em}{0ex}}\frac{1}{r}\\ \mathit{Where},\\ B\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathit{Magnitude}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{magnetic}\phantom{\rule{0.147em}{0ex}}\mathit{field}\\ r\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathit{Radius}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{circular}\phantom{\rule{0.147em}{0ex}}\mathit{wire}\end{array}$
• The strength of the magnetic field can be increased by taking a circular coil consisting of a number of turns of insulated copper wire closely wound together.
• If a circular coil has '$$n$$' turns, the magnetic field produced by this current-carrying circular coil will be '$$n$$' times as large as that produced by a circular loop of a single turn of wire.