Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as : (i) `V = a(x^2 - y^2)` (ii) `V = a x y`.

Determine the electric field strength vector if the potential of this

1.	Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as : (i) `V = a(x^2 - y^2)` (ii) `V = a x y`.
Answer» (i) As `V = a(x^2 - y^2)`, `E_x = - (del V)/(del x) = - (del)/(del x)a(x^2 - y^2) = -2 a x` and `E_y = -(del V)/(del y) = + 2 a y` `:. vec E = E_x hat i + E_y hat j = - 2 a x hat i + 2a y hat j = - 2 a(x hat i - y hat j)` (ii) As `V = a x y`, `E_x = (del V)/(del x) = - a y` and `E_y = -(del V)/(del y) = - a x` `:. vec E = E_x hat i + E_y hat j= - a y hat i - a x hat j = - a (y hat i + x hat j)`.

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Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as : (i) `V = a(x^2 - y^2)` (ii) `V = a x y`.

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