Electric Flux Density for Various Charge Distributions

Electric Flux Density for Various Charge Distributions

AU : Dec.-08, May-11

• Let us obtain the expression for  considering various types of charge distributions.

1. Line Charge

• Consider a line charge having uniform charge density of ρL C/m. Then the total charge along the line is given by,

• If the line charge is infinite then   is derived as,

2. Surface Charge

• Consider a sheet of charge having uniform charge density of ρs C/m². Then the total charge on the surface is given by,

• The integration is over the surface S and is a double integral.

• If the sheet of charge is infinite then   is derived as,

3. Volume Charge

Consider a charge enclosed by a volume, with a uniform charge density of p, C/m3. Then the total charge enclosed by the volume is given by,

Ex. 3.5.1 Determine  at (2, 0, 3) if there is a point charge -4 mC at (3, 0, 0) and a linecharge 2nmС/m along the y-axis.

AU May-11, Marks &

Sol. : Due to point charge at (3, 0, 0),

The line charge is along y axis so there can not be any component at   along y direction.

Let point on line charge is (0, y, 0) and P (2, 0, 3). 

Ex. 3.5.2 A uniform surface charge of ρs =2 μC/m² is situated at z = 2 plane. What is the value of flux density at P (1, 1, 1) m?

AU: Dec.-08, Marks 6

Sol. : Ps = 2 μC/m, z = 2 m plane, P (1, 1, 1).

Examples for Practice

Ex. 3.5.3 A point charge of 30 nC is located at origin, while plane y = 4 carries a charge 12 nC/m2. Find electric flux intensity at (0, - 4, 3)

Ex. 3.5.4 Find   in cartesian co-ordinate system at point P (6, 8, - 10) due to a) A point charge of 40 mC at the origin, b) A uniform line charge of ρL = 40 µ C/m on the z-axis and c) A uniform surface charge of density ρS = 57.2 µ C/m² on the plane x = 12 m.

Ex. 3.5.5 A point charge of 6 pC is located at the origin, a uniform line charge density of 180 nC/m lies along x-axis and uniform shed: of charge equal to 25 nC/m2 lies in the z = 0 plane. Find  at B (1, 2, 4) and iii) Total electric flux leauing the surface of the sphere of 4 m radius centered at the origin.