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QPages 141-142: Q3: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q3 Solution: Show that there can be no net charge in a region in which the…

Show that there can be no net charge in a region in which the electric field is uniform at all points.

Step-by-Step Verified Solution

**Answer:** If the electric field is uniform, the net charge in the region is zero. **Step-by-Step Explanation:** For a uniform field E⃗=constant\vec{E} = \text{constant}, consider any closed surface. The flux through the surface is zero (field lines entering equal field lines leaving). By Gauss's law, Φ=Qenclosed/ϵ0=0\Phi = Q_{enclosed}/\epsilon_0 = 0, so Qenclosed=0Q_{enclosed} = 0. Hence, there can be no net charge in a region of uniform electric field .

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