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physics12
- 4
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Homework Statement
gradient(1/r) = r(hat) / r^2
Homework Equations
r = (x-x')i + (y-y')j + (z-z')k
[Mentor Note -- Poster was reminded to always show effort on schoolwork questions]
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Yes it is. 1/r decreases with increasing r.kunu said:but this negative
The gradient of a function is a vector that points in the direction of maximum increase of the function at a particular point. It is also known as the slope or the rate of change of the function.
The gradient is calculated by taking the partial derivatives of the function with respect to each variable and creating a vector with these values. For a function of two variables, the gradient can be represented as ∇f(x,y) = (∂f/∂x, ∂f/∂y).
The "1/r" term represents the distance between the point where the gradient is being calculated and the point where the function is being evaluated. It is typically used in situations where the function is dependent on the distance from a specific point, such as in gravitational or electrical fields.
The gradient is commonly used in physics and engineering to determine the direction and magnitude of a physical quantity, such as force or potential energy. It is also used in vector calculus to solve problems related to motion, heat flow, and fluid mechanics.
Yes, the gradient can be negative. A negative gradient indicates that the function is decreasing in the direction of the gradient. In other words, the function is decreasing as you move in the direction of maximum decrease indicated by the negative gradient vector.