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Explain electric field and also electric...

Explain electric field and also electric field is point charge.

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If a small planar element of area `DeltaS` is place normal to `vecE` at a point, the number of field line, crossing it is proportional to `vecE.DeltavecS`.
Suppose we tilt the area element by angle `theta` , the `DeltaS` number of field lines crossing AS is proportiona to `EDeltaS cos theta`.
When `theta = 90^(@)`, field lines will be parallel tc surface and will not cross it at all.
When `theta = 0^(@)` , field lines will be normal to surface as shown in figure.

The vector associated with every area element of a closed surface is taken to be in the direction of the outward normal. Thus, the area element vector `DeltavecS` at a point on a closed surface equals `DeltaS hatn` where `DeltaS` is the magnitude of the area element and h is a unit vector in the direction of outward normal at that point. Electric flux is no. of electric field lines passing through or associated with the surface placed in electric field.
`therefore` Electric flux `Deltaphi` through an area element `DeltavecS` is `Deltaphi = vecE.DeltavecS = E DeltaS cos theta` , the angle `theta` here is the angle between `vecE` and `vecS`.
`phi = vecE.DeltavecS`
`=EDeltaS cos theta`
where `theta` is angle between `vecE` and `DeltavecS`
SI unit of electric flux is `Nm^(2)C^(-1)` or Vm and it is a scalar quantity.
Definition of electric.flux : "Electric flux associated with any area is areal integration of vector electric field on that area".
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Knowledge Check

  • In electric dipole is placed in an electric field of a point charge, then........

    A
    (A) the resultant force acting on the dipole is always zero.
    B
    (B) the resultant force acting on the dipole may be zero.
    C
    (c) torque acting on it may be zero.
    D
    (D) torque acting on it is always zero.
  • In a certain region, the electric potential is given by the formula V(x ,y, z) = 6xy - y + 2yz Find the components of electric field and the vector electric field at point (1, 1, 0) in this field. Find the vector of electric at (1, 1, 0).

    A
    `-(6hati+9hatj+hatk)`
    B
    `-(3hati+5hatj+3hatk)`
    C
    `-(6hati+5hatj+2hatk)`
    D
    `-(2hati+3hatj+hatk)`
  • An electric dipole is placed in an uniform electric field of a point charge, then ........

    A
    the resultant force acting on the dipole is always zero.
    B
    the resultant force acting on the dipole may be zero.
    C
    torque acting on it may be zero.
    D
    torque acting on it is always zero.
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