Suppose E = (x3y2, −y3x2, x3y3) and B = (ex, ey, ez ). Determine which (if any) vector fieldis solenoidal and explain why.[5 marks]END OF PAPER3
Question
Solution 1
To determine if a vector field is solenoidal, we need to check if the divergence of the vector field is zero. The divergence of a vector field F = (P, Q, R) is given by ∇.F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
- For E = (x^3y^2, -y^3x^2, x^3*y^3), the divergence is:
∇.E = ∂(x^3y^2)/∂x + ∂(-y^3x^2)/∂y + ∂ Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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