By Squadron Leader Zahid Mir CS&IT Department , Superior University PHY-AP -08 Electric Flux By Squadron Leader Zahid Mir CS&IT Department , Superior University

Flux Flux is the property of every vector field. Flux means “ T o Flow”. It is the measure of the “flow” or penetration of the field vectors through an imaginary fixed surface in the field. Flux is the rate at which field lines passes through the surface area.

Fluid Flow When the area A is perpendicular to the flow velocity v, the volume flow rate is given as; dV = v A dt

Fluid Flow (Contd) When the rectangle is tilted at an angle so that its face is not perpendicular to v, the area that counts is the shadow area that we see when we look in the direction of v. The area that is outlined in red and labeled A˩ in the figure is the projection of the area A onto a surface perpendicular to v.

Fluid Flow (Contd) Two sides of the projected rectangle have the same length as the original one, but the other two are foreshortened by a factor cosф , so the projected area A˩ is equal to Acosф.

Electric Flux Electric flux through the area held perpendicular to the electric field is the product of the field magnitude E and area A. фE = EA Increasing the area means more lines of E pass through the area and hence increase in flux. Stronger field means more closely spaced lines of E and therefore more lines per unit area, so again the flux increases.

Electric Flux (Contd) If the area is not perpendicular to field E, then a fewer field lines pass through it. In this case the area that counts is the silhouette area (A˩)that we see when looking in the direction of E.

Positive & Negative Flux We can represent the direction of a vector area A by using the unit vector perpendicular to the area; A surface has two sides, so there are two possible directions of and A. If the direction of A is outward normal then the flux is known as positive flux, and if the direction of A is normal inward then it is negative. Thus flux leaving the volume enclosed by the surface is considered positive, and the flux entering the volume enclosed is negative.

Flux through Irregular Surface in a Non-Uniform Electric Field Consider an arbitrary closed surface immersed in a non-uniform electric field. We divide the surface into small squares each of area ∆A. The direction of vector area ∆A is taken as the outward drawn normal to the surface. The element area ∆A is so small that E may be taken as constant for all points on the given square.

By summing the contributions of all the elements, we obtain the total flux through the surface.

The vectors points in different directions for the various surface elements, but at each point they are normal to the surface and, by convention, always point outward. At the element labeled (1), the field lines are crossing the surface from the inside to the outside and θ < 900; hence flux through this element is positive. For element (2) the field lines graze the surface (perpendicular to the vector ∆Ai ); thus θ = 900 and the flux is zero. For element (3), where the field lines crossing the surface from outside to inside, 1800 > θ > 900 and the flux is negative.

The net flux through the surface is proportional to the net number of lines leaving the surface. Net number means the number leaving the surface minus number entering the surface. If more lines are leaving than entering, then the net flux is positive. If more lines are entering than leaving, the net flux is negative. This surface integral indicates that the surface is to be divided into infinitesimal elements of area dA and the scalar quantity E.dA is to be evaluated for each element and summed over the entire surface.