Question

Consider a uniform electric field $E=3\times {10}^3$ $\hat{i}$ N/C. (a) What is the flux of this field through a square of $10$ cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a ${60}^o$ angle with the x-axis?

Answer 1

Area $A=(0.1{)}^2=0.01m^2$

Flux $\varphi =EA\cos \theta$

$\left(i\right)\theta =0^o$

$\varphi =3\times {10}^3\times 0.01\times \cos 0^o$

$⟹\varphi =30N{m}^2/C$

$\left(i\right)\theta ={60}^o$

$\varphi =3\times {10}^3\times 0.01\times \frac{1}{2}$

$⟹\varphi =15N{m}^2/C$