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What is a divergence of vector field. Express it in cartesian, spherical and cylindrical coordinates
1 Answer
written 7.1 years ago by | • modified 6.1 years ago |
The rate of change of a vector field is complex. The divergence of a vector field indicates how much the vector field spreads out from a certain point. The divergence of a vector is scalar.
If →B=Bxˆix+Byˆiy+Bzˆiz
Its divergence is written as →∇.→B=∂Bx∂x+∂By∂y+∂Bz∂z
In cylindrical coordinates, the field is written as→B=Brˆrx+Bϕˆiϕ+Bzˆiz
The divergence of the field is →∇.→B=1r∂∂r(rBr)+1r∂Bϕ∂ϕ+∂Bz∂z
In spherical coordinates, →B=Brˆrx+Bθˆiθ+Bϕˆiϕ
the divergence of a vector field is given by →∇.→B=1r2∂∂r(r2Br)+1rsinθ∂∂θ(sinθBθ)+1rsinθ∂Bϕ∂ϕ