An electric field of intensity 4.27 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if the following conditions are true.
(a) The plane is parallel to the yz-plane.
(b) The plane is parallel to the xy-plane.
(c) The plane contains the y-axis, and its normal makes an angle of 41.7° with the x-axis.
(a) In this case, the E field is perpendicular to the plane of the surface. Multiply the field strength by the area.
(b) In this case, the E field is parallel to the surface and the flux is zero.
(c) E*(Area)*(cos41.7) = ?
To calculate the electric flux through a rectangular plane, we can use the formula:
Flux = Electric field * Area * cos(θ)
where Flux is the electric flux, Electric field is the intensity of the electric field, Area is the area of the plane, and θ is the angle between the electric field and the normal to the plane.
(a) The plane is parallel to the yz-plane:
In this case, the plane is perpendicular to the x-axis, so the angle between the electric field and the normal to the plane is 90 degrees. Therefore, cos(90) = 0.
Flux = Electric field * Area * cos(θ)
= 4.27 kN/C * 0.350 m * 0
= 0
So, the electric flux through the plane parallel to the yz-plane is 0.
(b) The plane is parallel to the xy-plane:
In this case, the plane is perpendicular to the z-axis. Therefore, the angle between the electric field and the normal to the plane is also 90 degrees. Hence, cos(90) = 0.
Flux = Electric field * Area * cos(θ)
= 4.27 kN/C * 0.700 m * 0
= 0
So, the electric flux through the plane parallel to the xy-plane is also 0.
(c) The plane contains the y-axis, and its normal makes an angle of 41.7° with the x-axis:
In this case, the angle between the electric field and the normal to the plane is 41.7 degrees. Hence, cos(41.7) = 0.7538.
Flux = Electric field * Area * cos(θ)
= 4.27 kN/C * (0.350 m * 0.700 m) * 0.7538
= 1.446 kNm^2/C
So, the electric flux through the plane containing the y-axis and making an angle of 41.7 degrees with the x-axis is 1.446 kNm^2/C.