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July 17, 2020 • 16:03 pm 30 points

Mathematics (vector calculus) example: the quantity of any thing example: density example: temperature (at any instant) scalar field: the set of point

Mathematics (Vector Calculus) Example: The quantity of any thing Example: Density Example: Temperature (at any instant) Scalar Field: The set of points in any reaion Rand the vector function o at those poinis togemer s called a scalar field. Example : Temperature distribution in any medium. Example : Gravitational potential of a system of masses. Example: Electrostatic potential of charges of a system. Vector Point Function: Let R be a region of points in the space. If a scalar quantity V(P) or V(x, y. z) is obtained cOrresponding to every point P(x, y, z) by some rule, then V is called a vector point function in the egion R. Example: Velocity of any moving point of fiuid at any instant. Example: Force of electrical or magnetic intensity of any point of the electrical or magnetic field Vector Field: A vector field is a vector each of whos6 components is a scalar field, that is, a unction of our variables. We use any of the folowing notations for one: vo, y, z) = (v,, y, z), v,x, y, z), v,(x, y, z) vo, y. 2) =V,(x, y z)+V,, y, 2)+ v,x, y, z)hk Example: Velocity of moving fluid at any instant Example: Force of olectricity intensity Example : Force of magnetio intensity

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