A cube of side 0.4 m is placed in an electric field whose magnitude varies linearly with position: $E_x=150,x$ N/C, where $x$ is measured in metres from the left face of the cube. The cube’s faces are parallel to the coordinate axes and the left face is at $x=0$. Find the net electric flux through the cube.

Step-by-step solution

1. Write the field as $\mathbf{E}=150,x,\hat{\mathbf{i}}$ and compute its divergence: $abla!\cdot !\mathbf{E}=\frac{\partial E_x}{\partial x}=150,\text{N/C}$.
2. Use Gauss’s law in differential form: $Phi=in{t}_V(abla!cdot!\mathbf{E}),dV=150in{t}_{V}dV$.
3. Calculate the volume of the cube: $V=(0.4,\text{m}{)}^3=0.064,{\text{m}}^3$.
4. Multiply: $\Phi =150\times 0.064=9.6$ N⋅m²/C.

Concept tested: Divergence theorem for non‑uniform field

Published 3 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked