CBSE Class 12-science Answered

Toroid is a hollow circular ring (like a medu vadai) on which a large number of turns of a wire are wound.

The above figure represents a toroid wound with a wire carrying a current I. Consider path 1, by symmetry , if there is any field at all in this region, it will be tangent to the path at all point and  will equal the product will equal the product of B and the circumference d = 2pr of the path. The current through the path however is zero and hence from Ampere's law the field B must be zero.

Similarly, if there is any field at path 3, it will also be tangent to the path at all points. Each turn of the winding passes twice through the area bounded by this path, carrying equal currents in opposite directions. The net current though the area is therefore zero and hence B = 0 at all points of the path.

The field of the toroidal solenoid is therefore confined wholly to the space enclosed by the windings.

If we consider path 2, a circle of radius r, again by symmetry the field is tangent to the path and

Each turn of the winding passes once through the area bounded by path 2 and total current through the area is NI, where N is the total number of turns in the windings.

Using Ampere's law

If the radial thickness of the core is small, field is almost constant across the section.

Here 2pr circumferential length of to the toroid.

Conclusion:

Field outside the toroid and inside the core of the toroid is zero and within the toroid = m₀ni

Magnetic Field due to Solenoid

The magnetic field due to a section of the solenoid which has been stretched out for clarity. Only the interior semi-circular part is shown. Notice how the circular loops between neighbouring turns tend to cancel; hence magnetic field lines cannot be entirely confined within the core of a straight solenoid.

Hope this helps.

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