vector
scalar
A scalar is a magnitude that doesn't specify a direction. A vector is a magnitude where the direction is important and is specified.
The scalar product of two perpendicular vectors is zero.In classical mechanics we define the scalar product between two vector a and b as:a · b = |a| |b| cos(alpha)where |a| is the modulus of vector a and alpha is the angle between vectors a and b.If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.So finally a · b = 0.
Since you can represent that with a single number, it isn't a vector - just a scalar.
The equation that connects the scalar potential (V) and the vector potential (A) is given by: E = -∇V - ∂A/∂t, where E is the electric field, ∇ is the gradient operator, and ∂t represents the partial derivative with respect to time.
vector
No, the Laplacian is not a vector. It is a scalar operator used in mathematics and physics to describe the divergence of a gradient.
Temperature gradient is a vector quantity. It represents the rate of change in temperature with respect to position and has both magnitude and direction.
In a given region of space, the scalar potential is related to the electric field by the gradient of the scalar potential. The electric field is the negative gradient of the scalar potential. This means that the electric field points in the direction of the steepest decrease in the scalar potential.
No, electric potential is a scalar quantity, not a vector quantity.
Electric potential is a scalar.
Gravitational potential energy is a scalar. Gravity also has a vector energy cmV= 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.
Electrostatic potential is a scalar quantity. It represents the potential energy per unit charge at a given point in an electric field.
A scalar times a vector is a vector.
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.