Calculated the magnetic moment (in ) of a thin wire with a current A, wound tightly on a half a tore (see figure). The diameter of the cross section of the tore is equal to cm, and the number of turns is

Calculated the magnetic moment (in ) of a thin wire with a current A, wound tightly on a half a tore (see figure). The diameter of the cross section of the tore is equal to cm, and the number of turns is

1 Answer

127 votes

**(5)**

The magnetic moment of circular current is given by being the circulating current and is the area of cross-section; the direction is perpendicular to the plane of current. Now, for an element of toroid of length , its magnetic moment is along the direction of arrow as shown, of magnitude (perpendicular to its cross-section)=current area number of turns in the length

Resolving dM into components along and , we get and ; components along from neighbouring elements cancel out to zero, and components along are added. So

Putting the given values we get

127 votes

127