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What is the physical interpretation of gradient of a scalar field and directional derivative?
The elevation of points on a hill is a scalar 'field'. It can have a different value
at every point, but each one is a scalar value.
Imagine a lumpy bumpy irregular hill, and pick a point to talk about, say,
somewhere on the side of the hill.
At that point, the directional derivative of the elevation is the rate at which
the elevation changes leaving the point in that direction.
It has different values in different directions: If you're looking up the hill, then
the d.d. is positive in that direction; if you're looking down the hill, the d.d. is
negative in that direction. If you're looking along the side of the hill, the d.d.
could be zero, because the elevation doesn't change in that particular direction.
The directional derivative is a vector. The direction is whatever direction you're
talking about, and the magnitude is the rate of change in that direction.
The gradient is the vector that's simply the greatest positive directional derivative
at that point. Its direction is the direction of the steepest rise, and its magnitude
is the rate of rise in that direction.
If your hill is, say, a perfect cone, and you're on the side, then the gradient is the
vector from you straight toward the top, with magnitude equal to the slope of the
side of the cone. Any other vector is a directional derivative, with a smaller slope,
and it isn't the gradient.
What else can I help you with?
What is the physical interpretation of gradient of a scalar field and directional derivative and its application?
If you think of it as a hill, then the gradient points toward the top of the hill. With the same analogy, directional derivatives would tell the slope of the ground in a direction.
What is the physical application of third- and fourth-order derivatives with respect to distance e g first derivative is slope?
in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk
What is the physical name for fourth order derivatives?
We call "jerk" the third order derivative of position with respect to time, that is, the variation of acceleration. Some say that the derivative of jerk with respect to time (the fourth derivative of position with repsect to time) is called "jounce" or "snap".
What is physical interpretation of dot product?
it is physically the projection or shadow of a line on a plane...
What is physical meaning of gradient?
The gradient, at any point P:(x, y, z), of a scalar point function Φ(x, y, z) is a vector that is normal to that level surface of Φ(x, y, z) that passes through point P. The magnitude of the gradient is equal to the rate of change of Φ (with respect to distance) in the direction of the normal to the level surface at point P. Grad Φ, evaluated at a point P:(x0, y0, z0), is normal to the level surface Φ(x, y, z) = c passing through point P. The constant c is given by c = Φ(x0, y0, z0).
What is the physical interpretation of gradient of a scalar field and directional derivative and what are its applications?
say what
What is the physical interpretation of gradient of a scalar field and directional derivative and its application?
If you think of it as a hill, then the gradient points toward the top of the hill. With the same analogy, directional derivatives would tell the slope of the ground in a direction.
What does gradient mean in physics?
In physics, gradient refers to the rate of change of a physical quantity (such as temperature or pressure) in a particular direction. It represents how steeply a physical quantity changes over a distance. Mathematically, gradient is calculated as the change in the quantity divided by the distance over which the change occurs.
What is the physical significance of gradient define?
The gradient of a curve is the rate of change in the dependent variable relative to the independent variable.
What is the physical application of third- and fourth-order derivatives with respect to distance e g first derivative is slope?
in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk
What causes thigmotropism?
It is the directional response of a plant organ to physical contact with a solid object.
What is a synonym for gradient?
A graded change in the magnitude of some physical quantity or dimension
What is the physical name for fourth order derivatives?
We call "jerk" the third order derivative of position with respect to time, that is, the variation of acceleration. Some say that the derivative of jerk with respect to time (the fourth derivative of position with repsect to time) is called "jounce" or "snap".
What is the physical difference in the number of molecules between two regions of space A.concentration gradient B.plasma membrane C. receptor proteins D. phospholipid layer?
Concentration gradient.
What is the relationship between the concept of gradient energy and the movement of particles in a physical system?
The concept of gradient energy refers to the difference in energy levels between two points in a system. In a physical system, particles tend to move from areas of high energy to low energy, following the gradient. This movement is driven by the desire to reach a state of equilibrium where the energy levels are balanced.
Give the physical interpretation of the substantial derivative?
The first ∂/∂t term is called V the local derivative. The second ~· ∇ term is called the convective derivative. In steady flows, ∂/∂t =0, and only the convective derivative The substantial derivative has a physical meaning: the rate of change of a quantity (mass, energy, momentum) as experienced by an observer that is moving along with the flow. The observations made by a moving observer are affected by the stationary time-rate-of-change of the property (∂f/∂t), but what is observed also depends on where the observer goes as it floats along with the flow (v · ∇f). If the flow takes the observer into a region where, for example, the local energy is higher, then the observed amount of energy will be higher due to this change in location. The rate of change from the point of view of an observer floating along with a flow appears naturally in the equations of change.
How can one determine the velocity vector from a given position in a physical system?
To determine the velocity vector from a given position in a physical system, you can calculate the derivative of the position vector with respect to time. This derivative gives you the velocity vector, which represents the speed and direction of motion at that specific point in the system.
