Electric Field

• The region in which a charge experiences an electric force forms the electric field around the charge.
• The space around a charge Q gets modified so that when a test charge is brought into this region, it experiences a Coulomb force.
• The electric field exists around a charge irrespective of the presence of other charges.
• A positive charge placed in an electric field experiences a force in the direction of the field.
• A negative charge experiences a force in the opposite direction of the electric field.

The space surrounding an electric charge q in which another charge q₀ experiences a (electrostatic) force of attraction or repulsion, is called the electric field of the charge q.

OR

Electric field due to a charge Q at a point in space may be defined as the force that a unit positive charge would experience if placed at that point.

OR

The region surrounding an electric charge or a group of charges in which another charge experiences a force is called an electric field.

The electric field intensity at any point is the strength of the electric field at that point.

• It is defined as the force experienced by a unit positive charge placed at that point.

\[\vec{E}=\frac{\vec{F}}{q_0}=\frac{kq}{r^2}\hat{r}=\frac{kq}{r^3}\vec{r}\]

• The SI unit of E is NC⁻¹ (newtons per coulomb).

The charge Q that produces the electric field is called the source charge.

The charge q that tests the effect of the source charge is called the test charge.

\[\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}\]

The dimensional formula of the electric field E is:

E = \[\frac {F}{q_0}\] = \[\frac{[LMT^{-2}]}{[IT]}=[MLT^{-3}I^{-1}]\]

• An electric field is often represented by lines with arrowheads indicating the direction of the field.
• The direction of the electric field is the direction of force on a small positive charge.
• Electric lines of force are the paths along which a unit positive charge tends to move in the field.
• Electric lines of force are imaginary lines — they do not physically exist.
• For an isolated positive charge, lines of force are radially outward.
• For an isolated negative charge, lines of force are radially inward.
• The strength of an electric field is shown by how close the field lines are to one another.

• The test charge must be vanishingly small, so it does not modify the field of the source charge.
• The precise definition of the electric field uses the limiting condition:
  \[\vec E\] = \[\lim_{q\to0}\frac{\vec{F}}{q}\]
• E is independent of the test charge q because F is proportional to q, so the ratio F/q remains constant.

• The magnitude of E at a distance r from a point charge Q is the same at all points on a sphere of radius r.
• The direction of E is along the radius of the sphere — pointing away from the centre for a positive charge.
• This means the electric field of a point charge has spherical symmetry.