Question

What is the potential gradient? On which factors potential gradient depends?

Answer 1

Hint: A potential in physics can refer to either a scalar or a vector potential. It is a field defined in space in either scenario, from which many essential physical properties may be deduced. The gravitational potential and the electric potential are two examples of potentials that may be used to calculate the motion of gravitating or electrically charged things.

Complete step by step answer:
The local rate of change of the potential with respect to displacement, also known as the spatial derivative or gradient, is called a potential gradient. Because it leads to some sort of flow, this number commonly appears in equations of physical processes.
The most basic definition of a potential gradient F in one dimension is:
\[F = \dfrac{{{\phi _2} - {\phi _1}}}{{{x_2} - {x_1}}} = \dfrac{{\Delta \phi }}{{\Delta x}}{\mkern 1mu} \]
where\[\phi (x)\] is some sort of scalar potential and x represents displacement (not distance) in the x direction, the subscripts designate two distinct places \[{x_1},\;{x_2}\], and potentials at those points,\[{\phi _1}\; = \;\phi \left( {{x_1}} \right),\;{\phi _2}\; = \;\phi \left( {{x_2}} \right).\] The ratio of differences becomes a ratio of differentials when infinitesimal displacements are encountered: \[F = \dfrac{{{\text{d}}\phi }}{{{\text{d}}x}}\]
The electric potential gradient goes from ${x_1} - {x_2}$ in this example.
The gravitational field g is equivalent to the gradient in gravitational potential\[\Phi \] in the case of the conservative gravitational field g.
\[{\mathbf{g}} = - \nabla \Phi \]
Because the potential gradient and field are in opposing directions, the gravitational field and potential have opposite signs. As the potential grows, the gravitational field intensity falls, and vice versa.
The fall of potential across a potentiometer wire of length l is given by \[V = IR = \dfrac{{I\rho l}}{A}\]
Also \[K = \dfrac{V}{l} = \dfrac{{I\rho }}{A}\]
As a result, the potential gradient of a wire is determined by the following factors:
(I) \[K \propto I\] (current travelling through the potentiometer wire)
(ii) \[K \propto \rho \] (specific resistance of the potentiometer wire's material)
(iii) \[K \propto \dfrac{1}{A}\], where A is the potentiometer wire's cross-sectional area.

Note:
It makes no difference if a constant is put on since gradients in potentials correspond to physical fields (it is erased by the gradient operator, which includes partial differentiation). This means that there's no way of knowing what the "absolute value" of potential "is" — the zero value of potential is entirely arbitrary and may be set anywhere for the sake of convenience (even "at infinity"). This concept also applies to vector potentials, and it is used in both classical and gauge field theory.