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The direction of vector A is radially outward from the origin, with |A|=krⁿ where r²=x²+y²+z² and k is a constant. The value of n for which ∇· A=0 is
- −2
- 2
- 1
- 0
Correct answer: −2
Solution
The divergence of a vector field in spherical coordinates can be computed, and for a radially outward vector with magnitude proportional to r raised to the power of n, the condition for divergence to be zero leads to the requirement that n must equal -2. This ensures that the vector field behaves properly at infinity and does not contribute to divergence.
Related GATE Engineering Mathematics questions
- A vector field p and a scalar field r are given by
p = (2x² - 3xy + z²) î + (2y² - 3yz + x²) ĵ + (2z² - 3xz + x²) k̂
r = 6x² + 4y² - z² - 9xyz - 2xy + 3xz - yz
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
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