Question

What is net charge in the region where the electric field is uniform at all points..

Answer 1

Gauss Law states that Flux of Electric field is equal to net charge enclosed ina region divided by epsilon-nought. Now, since the electric field in a region is a constant, which means that the integral of E.ds is also a constant, hence q is equal to zero

Answer 2

Answer: The electric field is same in all points, the net charge in this region will be zero.  

Solution:  

The net charge in the region is found according to the Gauss theorem which is given as follows –

As we know that according to the Gauss theorem, the electric field has flux which is known as the electric flux and is a measure of charge in totality enclosed in a given region.  

Gauss theorem –Electric Flux = $\bold{\frac{Q_{n e t}}{\varepsilon_{0}}}$

Now the $\int E . d s=\frac{Q_{n e t}}{\varepsilon_{0}}$  

Since the electric field in an enclosed space is constant, we have

$\int E_{\text { constant }} \cdot d s=\frac{Q_{\text {net}}}{\varepsilon_{0}}$

$\begin{array}{l}{0=\frac{Q_{n e t}}{\varepsilon_{0}}} \\ {Q_{n e t}=0 \times \varepsilon_{0}} \\ \bold{{Q_{n e t}=0}\end{array}}$