CBSE Class 12 · 2011 · All India · Magnetic Effects of CurrentLong Answer

(a) Take a rectangular amperian loop with one side of length $L$ inside the solenoid (parallel to the axis) and the opposite side outside where $B=0$; the short sides contribute nothing. Then $\oint \vec{B}\cdot d\vec{\ell }=BL$, and the enclosed current is $nLI$, so (b) A toroid is a solenoid bent into a ring with no ends; its field lines are closed circles entirely within the core, whereas a straight solenoid's lines emerge from its ends and spread outside. (c) Increase the number of turns per unit length $n$, increase the current, and insert a soft-iron core.