The Helmholtz Coils are formed by a pair of conducting circular coils with many turns, each carrying a current . The coils are separated by a distance equal to the radius of the circular loops. This design produces a very uniform field in the center, it was first proposed by the German physicist Hermann von Helmholtz.
A compass is placed in the center of the Helmholtz Coils. When the current in the coils is zero, the needle of the compass points to the north. Because the horizontal component of the earth’s magnetic field is in the North-South direction. However, when an electrical current flows through the coils, a homogeneous magnetic field in the East-West direction is produced in the mid-plane between the two circular coils.
The compass needle will turn to the direction of the resultant vector of the sum of the magnetic field of the earth and the field of the coil .
With the increase of the current in the coils, the needle turns in the East-West direction.
is the sum of vectors and :
and the magnitude is
a) b) c)