For a position vector r = x î + y ĵ + z k̂ the norm of the vector can be defined as |r| = √(x² + y² + z²). Given a function ϕ = ln|r|, its gradient ∇ϕ is

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Accepted Answer

r/(r·r). The gradient of the function ϕ = ln|r| involves the derivative of the logarithm of the norm of the vector, which leads to a result that is proportional to the vector itself divided by the square of its magnitude. This is consistent with the formula for the gradient of a logarithmic function, resulting in the correct option being r/(r·r).

For a position vector r = x î + y ĵ + z k̂ the norm of the vector can be defined as |r| = √(x² + y² + z²). Given a function ϕ = ln|r|, its gradient ∇ϕ is

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