Physics - Electrostatics Question with Solution | TestHub

In non uniform electric field force on dipole

$$\begin{array}{rlrlrl}& F=\vec{p}\cdot \frac{\vec{d}\in }{dr};\vec{E}=4x{y}^2\hat{i}+4x^{2}y\hat{j}& \frac{d\in }{dx}=4y^2\hat{i}+8xy\hat{j};\frac{d\in }{dy}=8y\hat{i}+4x^2\hat{j}& F_x=\vec{p}\cdot \frac{\vec{d}\in }{dx}=4p{y}^2;F_y=\vec{p}\cdot \frac{\vec{d}\in }{dy}=8xyp& F_{Net}=\sqrt{F_x^2+F_y^2}=\sqrt{16p^2{y}^4+64p^2{x}^2{y}^2}& =4py{\left(y^2+4x^2\right)}^{\frac{1}{2}}\end{array}$$