Question

The electric field in a region is given by ${\displaystyle \overrightarrow{\text{E}}=\frac{2}{5}{\text{E}}_0\hat{\text{i}}+\frac{3}{5}{\text{E}}_0\hat{\text{j}}}$ with ${\displaystyle {\text{E}}_0=4.0\times {10}^3\frac{\text{N}}{\text{C}}}$. The flux of this field through a rectangular surface area 0.4 m² parallel to the Y - Z plane is ______ Nm²C^-1.

पर्याय

• 620

• 640

• 660

• 680

Answer 1

The electric field in a region is given by ${\displaystyle \overrightarrow{\text{E}}=\frac{2}{5}{\text{E}}_0\hat{\text{i}}+\frac{3}{5}{\text{E}}_0\hat{\text{j}}}$ with ${\displaystyle {\text{E}}_0=4.0\times {10}^3\frac{\text{N}}{\text{C}}}$. The flux of this field through a rectangular surface area 0.4 m² parallel to the Y - Z plane is 640 Nm²C^-1.

Explanation:

Flux, Φ = ${\displaystyle \overrightarrow{\text{E}}·\overrightarrow{\text{A}}=[\frac{2}{5}{\text{E}}_0\hat{\text{i}}+\frac{3}{5}{\text{E}}_0\hat{\text{j}}].\text{A}}$

= ${\displaystyle \frac{{\text{E}}_0}{5}(2\hat{\text{i}}+3\hat{\text{j}}).\left(0.4\hat{\text{i}}\right)}$

= ${\displaystyle \frac{4000}{5}(2\times 0.4)}$

= 640 Nm²C^-1