A conductor carries a current of 6.0 A along the closed path abcdefgha involving 8 of the 12 edges of a cube of side 10 cm as shown in the figure. We have to answer (a) why one can regard this as the superposition of three square loops: bcfgb, abgha, and cdefc? (b) By using the superposition we have to find the magnetic dipole moment of the closed path. (c) We have to calculate at the points , and

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A conductor carries a current of 6.0 A along the closed path abcdefgha involving 8 of the 12 edges of a cube of side 10 cm as shown in the figure. We imagine that on the edge bg a current of 6.0 A is flowing from b to g , and a current of 6.0 A is flowing from g to b. similarly, we imagine that on the edge cf a current of 6.0 A is flowing from c to f and a current of 6.0 a is flowing in the reverse direction from f to c.

The closed current loop

abcdefgha becomes equivalent to three square current loops bcfgb, abgha, and cdefc.

We replace each closed current loop by its equivalent magnetic dipole moment and determine the magnetic dipole moment of the loop

abcdefgha as the superposition of the dipole moments for the loops bcfgb, abgha, and cdefc.

As the length of each edge of the cube is 0.1 m and a current of 6.0 A is flowing in current loops, the equivalent magnetic dipole moments are:

The equivalent magnetic dipole moment of the loop abcdefgha will therefore be given by the superposition of the three dipole moments and will be

The magnetic field at the point , as it is on the axis of the dipole and is at a distance d far compared to the dimension of the dipole, will be given by the expression

The magnetic field at the point , as it is on the bisector to the dipole and is at a distance d far from the dimension of the dipole, will be given by the expression