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Given the potential V=2x2y−5zx and a point P(-4 , 3 , 6). Find V, E, D and ρv at P.
1 Answer
written 8.2 years ago by |
To find V at P:
V|(−4,3,6)=2(−4)2(3)−5(6)(−4)=216v
To find ˉE:
ˉE=−∇v=−[dvdx¯ax+dvdy¯ay+dvdz¯az]ˉE=−[(4×y−5z)¯ax+(2×2)¯ay+(−5x)¯az]ˉE=−4xy+5z¯ax−2x2¯ay+5x¯azˉE|(−4,3,6)=−4(−4)(3)+5(6)¯ax−2(−4)2ay+5(−4)¯az=78¯ax−32ay−20¯az
To find ˉD:
ˉD=εoˉEˉD=εo[78¯ax−32ay−20¯az]ˉD|(−4,3,6)=εo×E|(−4,3,6)