Electric Flux

Electric Flux

Electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface.

• The orientation of area element decides the amount of electric flux. Thus, the area element is a vector.

• The vector associated with every area element of a closed surface is taken to be in the direction of the outward normal.

• Area element vector ΔS = ΔSn̂, ΔS is magnitude of area element and n̂ is unit vectorin the direction of outward normal.

• Electric flux, Δφ = EΔS = E ΔScosθ, θ is angle between E and ΔS.

• Unit of electric flux is NC-1m2.

• Total flux through a surface, φ ≈ Σ EΔS

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Electric Dipole

An electric dipole is a pair of equal and opposite point charges q and –q, separated by a distance of 2a.

• Direction from –q to q is the direction of the dipole.

• The mid-point of locations of –q and q is called the center of the dipole.

• Total charge of an electric dipole is zero but since the charges are separated by some distance the electric field do not cancel out.

• Dipole moment is the mathematical product of the separation of the ends of a dipole and the magnitude of the charges (2a x q).

• Some molecules like H2O, have permanent dipole moment as their charges do not coincide. These molecules are called polar molecules.

• Permanent dipoles have a dipole moment irrespective of any external Electric field.

Electric field of an electric dipole

Electric field of an electric dipole at a point in space depends upon the position of the point.

• The dipole field at a point is inversely proportional to the cube of distance from the center to the point.

• For a very small dipole, the 2a approaches zero. This is called point dipole.

Example:

To calculate electric field at mid point of line joining two charges 3 & -3 μC, which are 20 cm apart, we can use the formula for electric field of a dipole on an axis.

Dipole in a uniform electric field

When two charges in a dipole are separated by some distance, the forces acting at different points result in torque on the dipole. The torque tries to align the dipole with electric field. Once aligned, the torque becomes 0.

• Magnitude of torque = qE x 2a sinθ = 2qaE sinθ = pEsinθ.

• Direction of the torque= normal to the plane coming outwards.