Harmonic Functions:
A function is said to be harmonic if it satisfies Laplace's equation, which is given by:



where V is the scalar function and ∇² is the Laplacian operator.

Explanation:
To understand why the correct answer is option 'C', let's consider the other options and their implications.

a) Curl(Grad V) = 0:
This equation represents the curl of the gradient of a scalar function V. In three-dimensional space, the curl of the gradient is always zero. However, this condition does not necessarily imply that the function is harmonic. There are non-harmonic functions for which the curl of the gradient is also zero.

b) Div(Curl V) = 0:
This equation represents the divergence of the curl of a vector field V. In general, the divergence of the curl is not always zero. This condition does not guarantee that the function is harmonic.

d) Grad(Curl V) = 0:
This equation represents the gradient of the curl of a vector field V. Just like the curl of the gradient, the gradient of the curl is always zero in three-dimensional space. However, this condition does not imply that the function is harmonic.

c) Div(Grad V) = 0:
This equation represents the divergence of the gradient of a scalar function V. By applying the divergence operator to the gradient, we obtain the Laplacian of V. Therefore, Div(Grad V) = ∇²V. Since the Laplacian of V is zero for a harmonic function, this condition ensures that the function is harmonic.

Conclusion:
The correct answer is option 'C' because Div(Grad V) = 0 implies that the function satisfies Laplace's equation, which is the defining condition for a function to be harmonic. The other options do not guarantee that the function is harmonic.