( ), B = Thus, the magnetic field at any point P in the open space inside the toroid is zero. We shall now show that magnetic field at Q is likewise zero. Let the magnetic field along loop be B . Once again from Ampere’s law L = π r .
However, from the sectional cut, we see that the current coming out of the plane of the paper is cancelled exactly by the current going into it. Thus, I e = , and B = . Let the magnetic field inside the solenoid be B . We shall now consider the magnetic field at S.
Once again we employ Ampere’s law in the form of Eq. [ . (a)]. We find, L = π r.
The current enclosed I e is (for N turns of toroidal coil) N I . B ( π r ) = µ NI FIGURE . (a) A toroid carrying a current I . (b) A sectional view of the toroid.
The magnetic field can be obtained at an arbitrary distance r from the centre O of the toroid by Ampere’s circuital law. The dashed lines labelled , and are three circular Amperian loops.