Find the potential `varphi (x,y)` of an electrostatic field `E = 2axyi + a (x^(4) - y^(2)) j`, where `a` is a constant, `I` and `J` are the unit vectors of the `x` and `y` axes.

Find the potential `varphi (x,y)` of an electrostatic field `E = 2axyi

1.	Find the potential `varphi (x,y)` of an electrostatic field `E = 2axyi + a (x^(4) - y^(2)) j`, where `a` is a constant, `I` and `J` are the unit vectors of the `x` and `y` axes.
Answer» `-d varphi = vec(E) . vec(dr) = [2 a xy vec(i) + 2(x^(2) - y^(2)) vec(i)] . [dx vec(i) + dy vec(i)]` or, `d varphi = 2a xy dx + a(x^(2) - y^(2)) dy = ad (x^(2) y) - ay^(2) dy` On intergating, we get `varphi = ay ((y^(2))/(3) - x^(2)) + C`

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Find the potential `varphi (x,y)` of an electrostatic field `E = 2axyi + a (x^(4) - y^(2)) j`, where `a` is a constant, `I` and `J` are the unit vectors of the `x` and `y` axes.

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