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scalar field: some function assigns a number to every location in space
vector field: " " " " vector " " " " "
plz explain with example
A scaler field has a single number assigned to each point in the field.
If the centre of a copper disc is heated while the edges are kept cool until an equilibrium is reached, you could calculate (in theory) the temperature at every point on the disc. The temperature is represented by a single number.
A vector field has a magnitude and direction assigned to each point in the field. Pull the plug in your bathtub and watch the water spiral down. At each point the water has a speed and direction it is a vector field.
Electric & magnetic fields are other examples of vector fields.
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when we heat a disc, heat also have a dirction towards edges then how it is scalar ?
post your equation
scalar in 2-D [eg a disc] might say:
\(T(x,y) = x^2 - y^3 + e^y\)
yes, silly and all in yur example, because heat might not distribute itself that way; but for every x and y value you will have a T(x,y)
that is a scalar function. at (0,0), you will have T = 1
next, again in simple 2D, we might have \(\vec E = < xy \ e^x, y + cos x>\)
this is a vector field. at (x,y) = (0,0), \(\vec E = <0,1>\)
from a scalar field you can build a vector field using the directional derivative/ gradient.... is that what you are looking at?!?!
what is differece between vector function and vector field ?
you can say: \(\vec f(x,y,z) = \vec f ( \vec r)\)
but why do you ask? do you have a specific example in mind?
you started with a question about vector and scalar fields.
to add to it:
In physical sciences, a field is a physical space that has a value for each point in space [and time actually].
i m confused about this whole topic thats why i was asked
i m confuse about vector function and vector field repressention?