Question

write down the expression of electric and magnetic field it terms of scalar and vector potential​

Answer 1

We can automatically satisfy Equation (2) by writing

$\displaystyle {\bf B} = \nabla\times {\bf A},$ (11)

where $ {\bf A}({\bf r},t)$ is termed the vector potential. Furthermore, we can automatically satisfy Equation (3) by writing

$\displaystyle {\bf E} = -\nabla\phi- \frac{\partial {\bf A}}{\partial t},$ (12)

where $ \phi({\bf r},t)$ is termed the scalar potential.

The previous prescription for expressing electric and magnetic fields in terms of the scalar and vector potentials does not uniquely define the potentials. Indeed, it can be seen that if $ {\bf A}\rightarrow {\bf A}-\nabla\psi$ and $ \phi\rightarrow \phi+\partial\psi/\partial t$ , where $ \psi({\bf r},t)$ is an arbitrary scalar field, then the associated electric and magnetic fields are unaffected. The root of the problem lies in the fact that Equation (11) specifies the curl of the vector potential, but leaves the divergence of this vector field completely unspecified. We can make our prescriptio and please mark me brainlist

Answer 2

Scalar potentials are generally observed under static field conditions where as vector potentials are observed under dynamic conditions.....Thus, a vector potational is a vector field whose curl is a given vector .This is analogues to a scalar potential, which is a scalar field whose gradiant is a given vector field.

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