Electric Dipole - Potential At a Point Due To Electric Dipole.
- An electric dipole consists of two point charges of equal magnitude but of opposite sign and separated by a small distance.
- Consider an electric dipole centered at origin and placed in z – axis as shown in the figure:
- The potential (V) at point P is given as:
- If the distance between the charges (d) is very small as compared to the distance of the point P from the origin i.e.
If r >> d,
r2 – r1 ≅ d cosθ ; r1 ≅ r2 = r ; r1r2 ≅ r2
Substituting the values in the above equation, the potential at point P becomes:
- Electric field intensity (E) is the negative gradient of Electric Potential (V).
- The expressions for electric potential (V) and field intensity (E) above are only valid for a dipole centered at the origin and aligned with the z-axis.
- To determine the fields produced by any arbitrary location and alignment, we first need to define a new quantity p, called the Dipole Moment.
p = Q d
- Since the distance d is a vector quantity, the dipole moment p is also a vector quantity.
- Dipole moment p is a measure of the strength of the dipole and indicates its direction.
- Vector d is a directed distance that extends from negative charge (- Q) to positive charge (+ Q). This directed distance vector d thus describes the distance between the dipole charges, as well as the orientation of the charges.
d = | d | ad
Where | d | is the distance between the charges and ad defines the orientation or direction of the dipole.
- Say a dipole is aligned along z – axis, then directed distance d is given as:
d = | d | az
From the above diagram it’s clear that:
az . ar = cosθ
Hence the expression can be written as:
Q d cosθ = Q | d | az . ar = Q d. ar = p . ar
- Hence electric potential (V) due to a electric dipole centered at origin and aligned with the z axis is rewritten as:
- The above expression no doubt is applicable for all and any dipole moments p, but is valid for dipoles centered at origin.
- Electric potential (V) at point P with a position vector r due to a dipole centered at a point with position vector r1 is given as:
- Gauss's Law - Theory.
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- Gauss's Law - Application To An Infinite Line Charge.
- Gauss's Law - Application To An Infinite Sheet Charge.
- Gauss's Law - Application To a Uniformly Charged Sphere.
- Numericals / Solved Examples - Gauss's Law.
- Scalar Electric Potential / Electrostatic Potential (V).
- Relationship Between Electric Field Intensity (E) and Electrostatic Potential (V).
- Electric Potential Due To a Circular Disk.
- Electric Dipole.
- Numericals / Solved Examples - Electric Potential and Electric Dipole.
- Energy Density In Electrostatic Field / Work Done To Assemble Charges.
- Numericals / Solved Examples - Electrostatic Energy and Energy Density.
- Numericals / Solved Examples - Gauss's law...
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