The x commponent of the electric field is E x dVdx ddx20 Vm 2 x 2 30 Vm 2 ....

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The x-commponent of the electric field is,

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â E_x = dV/dx

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = d/dx[(2.0 V/m²)x² - (3.0 V/m²)y²]

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (2.0 V/m²)(2x)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (4.0 V/m²)x

The y-commponent of the electric field is,

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â E_y = dV/dy

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = d/dy[(2.0 V/m²)x² - (3.0 V/m²)y²]

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = -(3.0 V/m²)(2y)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = -(6.0 V/m²)y

Thus, the vector form of the electric field is,

Â Â Â Â Â Â Â Â E = E_x + E_y

Â Â Â Â Â Â Â Â Â Â Â = [(4.0 V/m²)x] i - [(6.0 V/m²)y] j

Here, i and j are unit vectors along the x and y axis respectively.

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