Electric Field Intensity is defined as the force experienced by a unit positive charge PLACED at that Point. Simply means that electric field is defined at a POINT.
Mathematically place a unit positive charge at the point of consideration and Understand the Force at that point. As electric field is a vector, its direction is the force experienced by positive charge. It simply means if the charge is negative the force will be in opposite direction.
Uniform electric field means that electric lines of forces are parallel and same magnitude in length, technically the E is same in magnitude & direction. While for non-uniform fields E is not same (may change in magnitude or direction) and is usually represented by non-parallel lines of forces.
Force on any charge placed in electric field F = qE
Dipole : Two equal and opposite charges kept at finite distance distance constitute a dipole.
Dipole Moment : it can be understood as strength of dipole. Mathematically it is give as vector quantity p = (2a) q Its unit is Coulomb meter. But the direction is from negative charge to positive charge.
To find the electric field due to DIPOLE on axial Line.
To find the electric field, (let us say at point P) we try to find the electric field due to both charges and then we add vectors.
Similarly for the equatorial line
We try to find the electric field and then add vectors as in diagram.
Then special cases of r > > a in both cases.
Now in next case we study the behavior of Dipole when placed in external uniform electric field. In such case.
Remember that since the field taken is uniform, and charges of DIPOLE (constant in magnitude) so both the charges will have exactly equal and opposite Forces. Thus net force on a dipole system in UNIFORM electric field is also ZERO.
Now if the dipole is neither parallel nor anti parallel to Electric field, then it will have a rotating force due to a couple. [Remember two equal and opposite forces constitute a Couple]
So to find the torque we multiply Force by perpendicular force
Torque = qE × (2a sin θ) = (2aq) × E sin θ = p × E sin θ
vector wise Τ = p × E
Torque is zero, when angle is either 0 or 180. Recall force is always ZERO
When force and torque both are zero. Then it has mechanical euilibrium
Now we find energy by ∫F.ds = ∫ T.dθ = ∫ pE sin θ. dθ = -pE cos θ = –p.E
IMPORTANT
we find that energy is MAXIMUM at 180, means unstable equilibrium; at 0 we have MINIMUM energy hence STABLE equilibrium.
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