Elements Of Electromagnetics Sadiku 7th Edition — Solution !!install!!

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In Cartesian coordinates, $\nabla V = \frac\partial V\partial x\mathbfa_x + \frac\partial V\partial y\mathbfa_y + \frac\partial V\partial z\mathbfa_z$. Therefore, $\mathbfE = -\frac\partial V\partial x\mathbfa_x - \frac\partial V\partial y\mathbfa_y - \frac\partial V\partial z\mathbfa_z$. Elements Of Electromagnetics Sadiku 7th Edition Solution

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Use Gauss’s law: ( \oint \mathbfD \cdot d\mathbfS = Q_\textenc ). Step 1 – Choose a spherical Gaussian surface of radius ( r < R ) (sphere radius ( R )). Step 2 – Charge enclosed = ( \rho \cdot \frac43\pi r^3 ), where ( \rho = \fracQ4\pi R^3/3 ). Step 3 – By symmetry, ( \mathbfD ) is radial and constant on the Gaussian surface. Step 4 – ( D \cdot 4\pi r^2 = Q_\textenc ) → solve for ( D ), then ( \mathbfE = \mathbfD/\varepsilon ).