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The direction of vector A is radially outward from the origin, with |A| = k rⁿ where r² = x² + y² + z² and k is a constant. The value of n for which ∇·A = 0 is

1. -2
2. 2
3. 1
4. 0

Correct answer: -2

Solution

The divergence of a radial vector field is calculated using the formula ∇·A = (1/r²)(∂/∂r)(r² A_r), where A_r is the radial component. For the given magnitude |A| = k rⁿ, setting n to -2 results in the divergence being zero, satisfying the condition ∇·A = 0.

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