Answer:
[tex]E = -40\hat{i} + 12\hat{j}[/tex]
Explanation:
Given that:
[tex]V=(4x^{2} - 2y^{2} ) V/m^{2}[/tex] --- (1)
To find:
Electric field at point (5,3) in xy plane.
Electric field in plane s is related to V by:
[tex]E_{s} =- \frac{\partial V}{\partial {S}}[/tex]
For xy plane:
[tex]E_{x} - \frac{\partial V}{\partial x} \\E_{y} - \frac{\partial V}{\partial y}[/tex]
Using (1) in above two equations
[tex]E_{x} = -\frac{\partial }{\partial x} (4x^{2} - 2y^{2})\\E_{x} = -8x\\E_{y} = -\frac{\partial }{\partial y} (4x^{2} - 2y^{2})\\E_{y} = 4y[/tex]
In vector form
[tex]E = E_{x}\hat{i} + E_{y}\hat{j} \\E = -8x\hat{i} + 4y\hat{j}[/tex]
at (5,3)
[tex]E = -40\hat{i} + 12\hat{j}[/tex]
