what do you mean by gradient of a scalar field? what do you mean by gradient of a scalar field?
Distance is a scalar. But displacement is a vector.
Since you can represent that with a single number, it isn't a vector - just a scalar.
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scalar
let A be the Vector potential and Q as the scalar potential
Electric potential is a scalar.
vector
it is a scalar quantity
Gravitational potential energy is a scalar. Gravity also has a vector energy cmV= cP.
Gradient means the vector derivative (Del) of a scalar quantity, e.g. for the Gravity Potenttial/scalar energy, Del-mGm/r= mw2R.
Potential energy is a scalar quantity. Energy is the sum of a scalar part and a vector part. Energy W is the product of velocity V and momentum P; W = [c+V]P =[ -V.P + cP]. The Potential energy is the scalar energy -V.P=-vmv = -mv^2.Physicists consider energy a scalar quantity, but that is incorrect, energy is a Quaternion quantity, a scalar and a vector . The vector energy is the "Dark Energy" is hidden in plain sight, cP.
Electrical Potential Energy is a scalar or real number. Ep = zc e2 /4pi r.Total Energy is a Quaternion, the sum of the real or potential energy and the vector energy, Ev= mcV;E = Es + Ev = zc e2 /4pi r + mcV where Ev = mcV and V is the vector velocity.
Because Electric field can be expressed as the gradient of a scalar. Curl of a gradient is always zero by rules of vector calculus.
scalar lol
Electric potential is a scalar quantity since work done and charge are scalars
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.