Answer to Question #97270 in Electricity and Magnetism for sushmita

Question

an electric field of magnitude 3.50 kn c is applied along the x-axis. calculate the electric flux through a rectangular plane 0.35m wide and 0.7m long a)if the plane is ||le to the yz plane b)if the plane is ||le to the XY plane and c)if the plane contain the y-axis and its normal make an angle of 40.8 degrees with the x-axis

Answer 1

a) The simplest case, because the plane is perpendicular to the field lines, i.e. the angle $\theta$ between the field lines and the normal to the surface is 0:

$$\Phi_E=E\cdot A\cdot\text{cos}\theta=3500\cdot0.35\cdot0.7\cdot1=\\=857.5\text{ Nm}^2/\text{C}.$$

b) Since now the angle between the normal and the field is 90 degrees, or the plane is parallel to the field lines, the flux is 0, because cosine of 90 degrees is 0.

c) We have all we need to know, i.e. the angle, so

$$\Phi_E=E\cdot A\cdot\text{cos}\theta=3500\cdot0.35\cdot0.7\cdot\text{cos}40.8^\circ=\\=649.1\text{ Nm}^2/\text{C}.$$