Determine the electric field strength vector if the potential of this field depends on x, coordinates as(a) `V = a (x^2 — y^2)` (b) `V = axy` where, a is a constant.

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 on x, coordinates as(a) `V = a (x^2 — y^2)` (b) `V = axy` where, a is a constant.
Answer» (a) Given, `varphi = a(x^(2) - y^(2))` So, `vec(E) = -vec(grad) varphi = -2a (x vec(i) - y vec(j))` The sought shape of field lines is as shown in fig of answersheet assuming `a gt 0` : (b) Since `varphi = axy` So, `vec(E) = -vec(grad) varphi = -ay vec(j) - ax vec(j)` Plot as shown in fig(b) of answersheet.

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Determine the electric field strength vector if the potential of this field depends on x, coordinates as(a) `V = a (x^2 — y^2)` (b) `V = axy` where, a is a constant.

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