Question

What is a toroid? Mention an expression for the magnetic field at a point inside a toroid?

Answer 1

Hint: The current carrying wire wound spirally in the form of helix about an axis is known as solenoid or coil .Magnetic field produced due to current carrying solenoid is fairly uniform over a small region in the middle of the coil. It acts just like a bar magnet having north and south poles and there are several methods used to determine the polarity of the solenoid.

Complete answer:
A solenoid bent into a circular shape to form a closed loop like structure is called toroid. A toroid is a hollow circular ring and in toroid the magnetic field inside and outside is zero. In electronic circuit’s toroid are used as inductors at low frequencies due to the requirement of large inductance at lower frequencies.

Magnetic field due to a toroid is given by the formula:
\[B=\dfrac{{{\mu }_{0}}NI}{2\pi r}\]
Where N= number of turns threading a curve long a field line inside the toroid.
              I= current which is flowing in each turn.
              r=radius of the toroid
If n is the number of turns per unit length of circle
$n=\dfrac{N}{2\pi r}$
Then the formula becomes :
$\begin{align}
  & B=\dfrac{{{\mu }_{0}}(2\pi rn)I}{2\pi r} \\
 & B={{\mu }_{0}}nI \\
\end{align}$
Outside the toroid at any point the number of turns per unit length is zero.
The magnetic field inside a toroid is zero.in the toroid the magnetic field is constant in magnitude and its direction is clockwise.

Note:
Students a toroid has more inductance than the solenoid with similar size and with same core material and in the core material of a toroid all the magnetic flux are present because the core of toroid as no ends .There is no polarity in the toroidal magnets and in ideal toroid the coils are circular. Helix rule is used to find the polarities of solenoid.