Three identical long solenoid P,Q and R are connected to each other as shown in fig. If the magnetic field at the centre of P is 2.0T, what would be the field (inT) at the centre of Q? Assume that the field due to any solenoid is confined within the volume of that solenoid only.

Explanation

As the solenoids are identical, the currents in Q and R will be the same and will be half the current in P. The magnetic field within a solenoid is given by B = `mu_0`ni. Hence the field in Q will be equal to the field in R and will be half the field in P i.e., will be 1.0 T.
Magnetic Field in a Toroid
(i) Toroid is like an endless cylindrical solenoid, i.e. if a long solenoid is bent round in the form of a closed ring, then it becomes a toroid.

(ii) Electrically insulated wire is wound uniformly over the toroid as shown in the firgure.
(iii) The thickness of toroid is kept small in comparison to its radius and the number of turns is kept very large.
(iv) When a current i is passed through the toroid, each turn of the toroid produces a magnetic field along the axis at its centre. Due to uniform distribution of turns this magnetic filed has same magnitude at their centres. Thus the magnetic lines of force inside the toroid are circular.
(v) The magnetic field inside a toroid at all points is same but outside the toroid it is zero.
(vi) If total number of turns in a toroid is N and R is its radius, then number of turns per unit length of the toroid will be
`n=(N)/(2piR)`
(vii) The magnetic field due to toroid is determined by Ampere’s law.
(viii) The magnetic field due to toroid is `B_(0)=mu_(0)"ni" or B_(0)=mu_(0)((N)/(2piR))i`
(ix) If a substance of permeability  is placed inside the toroid, then
`B=mu"ni"`
If `mu_(r)` is relative magnetic permeability of the substance , then
`B=mu_(r)mu_(0)"ni"`