Table of Contents
- 1 Why do we need magnetic potential vectors?
- 2 Why is magnetic scalar potential not a useful concept?
- 3 Why do we use vectors in electromagnetic fields?
- 4 What is the advantage of scalar potential formulation in electrostatics?
- 5 Why is magnetic vector potential a vector energy?
- 6 What does it mean to say that vector potential is undetermined?
Why do we need magnetic potential vectors?
Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A.
How scalar and vector potential applies in electromagnetic field?
The scalar potential can be used when the field is curl free. That is, for the magnetic field (whose rotational is equal to the current, according to Ampere’s Law) the scalar potential can only be used in regions without current. The potential vector can be used in all regions. Neither of the two potentials is unique.
Why is magnetic scalar potential not a useful concept?
In electricity and magnetism, we use the scalar potential to derive the electric field and the vector potential to derive the magnetic field because ∇⋅B=0 and ∇×E=0. Not because changing one field creates the other, or because one circulates round the other.
What is scalar potential of A vector?
Scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other.
Why do we use vectors in electromagnetic fields?
The widespread acceptance of vectors in electromagnetic field theory is due in part to the fact that they provide compact mathematical representations of complicated phenomena and allow for easy visualization and manipulation.
Is magnetic potential vector quantity?
The curl of magnetic vector potential is the magnetic field. It is a vector field. So electric fields and magnetic fields are vector quantities.
What is the advantage of scalar potential formulation in electrostatics?
What is the advantage of using the potential formulation over calculating electric field? Potential being a scalar is easier to deal with mathematically.
What is the scalar potential of a magnetic field?
The quantity in the above equation is known as the electric scalar potential. Magnetic fields generated by steady currents (and unsteady currents, for that matter) satisfy since the divergence of a curl is automatically zero.
Why is magnetic vector potential a vector energy?
So as I said before, just as the electric scalar potential is potential energy per unit charge, the magnetic vector potential is potential energy per unit element of current. But current has a direction, so the magnetic vector potential has to have three components. That’s why it’s a vector too.
Can scalar potential be multi valued?
Electric potential is single value since curl E =0. According to me magnetic scalar potential should be single valued ( since curl B=0) and the vector potential should be multi valued. I can just not get how scalar potential is multi valued . It should be single valued since curl B=0.
What does it mean to say that vector potential is undetermined?
In other words, the vector potential is undetermined to the gradient of a scalar field. This is just another way of saying that we are free to choose . Recall that the electric scalar potential is undetermined to an arbitrary additive constant, since the transformation leaves the electric field invariant in Eq. ( 316 ).