Question:
A plane \$x+2y=5\$ carries charge \$\rho_s=6nC/m^2\$. Determine electric field at \$(-1,0,1)\$.
My try:
At first, I calculated gradient
Let, \$\phi=x+2y-5\$
\$\begin{align}\\ \vec\nabla\phi&=\frac{\partial\phi}{\partial x}\hat a_x+\frac{\partial\phi}{\partial y}\hat a_y+\frac{\partial\phi}{\partial z}\hat a_z\\ &=\hat a_x+2\hat a_y \end{align}\\\$
We know, \$\vec E=\frac{\rho_s}{2\epsilon_0}\hat a_n\$, where \$\hat a_n\$ is the normal vector to the surface
Here, \$\hat a_n=\frac{\hat a_x+2\hat a_y}{\sqrt{1^2+2^2}}=\frac{1}{\sqrt{5}}(\hat a_x+2\hat a_y)\$
\$\begin{align}\\ \therefore\vec E&=\frac{6\times 10^{-9}}{2\times\epsilon_0}.\frac{1}{\sqrt{5}}(\hat a_x+2\hat a_y)\\ &=151.53\hat a_x+303.1\hat a_y\\ \end{align}\\\$
But, in my book answer is:\$=-151.53\hat a_x-303.1\hat a_y\$. I can't understand why there is minus sign. Please anyone check this.