Question

Find the volume charge density associated with a field given by D= (xy²)i + (yx²)j + (z) C/m²

Answer 1

The given electric field is associated with D =$(xy^{2}) \hat{i}+(yx^{2})\hat{j}+z\ c/m^{2}$

now , we have to find out volume charge density with the help of given field function , the relation between the Electric field and volume charge density is given by -

volume charge density is denoted by $\rho$ = ${\nabla}.D$

${\nabla}=\dfrac{\partial}{\partial x}\hat{i}+\dfrac{\partial}{\partial y}\hat{j}+\dfrac{\partial}{\partial z}\hat{k}$

$\rho$ $=\dfrac{\partial(xy^{2})}{\partial x}\hat{i}+\dfrac{\partial(yx^{2})}{\partial y}\hat{j}+\dfrac{\partial(z)}{\partial z}\hat{k}$

$\rho=y^{2}\hat{i}+x^{2}\hat{j}+\hat{k}$ $c/m^{3}$