Electric Dipole
If two charges of equal magnitude and opposite nature are present at a very small distance from each other, they form an electric dipole.
If two charges +q and - q are situated at a distance `2 l` (may be 2r or 2a).
`star` The midpoint between the two charges is called the center of electric dipole.
`star` The line joining these charges is called axial line.
`star` The line perpendicular to axial line and passing through the center is called equatorial line.
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| Electric Dipole |
Electric Dipole Moment
The product of the charge and the distance between them is called the dipole moment.
If we consider the distance 2a between the charges to be a vector whose direction is from -q to +q.
Then, from definition,
`\vec p = q (2\vec a)`
Unit of electric dipole moment = Coulomb \times meter
Dimensions of electric dipole moment = ` [M^0L^1T^1A^1]`
Examples of Electric Dipole
HCl, Nacl etc.
Electric Field Due to Electric Dipole
We will find the electric field on the axial line and equatorial line of the electric dipole.
Electric Field due to Dipole on Equatorial Line
Question: Derive an expression for an electric field due to an electric dipole at a point on equatorial line.
Two charges +q and -q forms an electric dipole. The mid point of dipole O is the center of the dipole. A line perpendicular to the axial line and passing through O is an equatorial line.
Let a point P on the equatorial line where we have to find the electric field due to the electric dipole.
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| Electric field due to dipole on equatorial line |
Electric field due to +q charge at point P is `E_{+q}`
`E_{+q} = \frac{K q}{(r^2 + a^2)`
Electric field due to -q charge at point P is `E_{-q}`
`E_{-q} = \frac{K q}{(r^2 - a^2)`
Two directions of the electric field at point P are not possible so we will use the components of the electric field.
The components of the electric field along y-axis are equal and opposite so they are cancel.
The components of the electric field along the x-axis are in the same direction so they will be added.
Thus, the resultant electric field due to both charges on point P
`E_P = E_{+q}cos\theta + E_{-q}cos\theta`
`E_P = 2 E_{+q}cos\theta` `(\because E_{+q} = E_{-q})`
`E_P = 2 \frac{K q }{(r^2 + a^2)} \frac{a}{(r^2 + a^2)^\frac{1}{2}}`
`E_P = \frac{K (q \times 2a) }{(r^2 + a^2)^\frac{3}{2}}`
`E_P = \frac{K p }{(r^2 + a^2)^\frac{3}{2}}` `{\because p = q\times 2a}`
For r >>> a, `(r^2 + a^2)^\frac{3}{2} \approx r^3`
`E_P = \frac{K p }{r^3}`
Vector form
`\vec E = - \frac{K \vec p}{r^3}`
It is clear that for equal distance r
`E_{\text{axial}} = 2 E_{\text{equatorial}}`
Thus,
`\star` The electric field intensity placed at the axis is twice the electric field at the point on the equatorial line of the electric dipole.
`\star` The direction of the electric field at a point on the axial line of the dipole is in the same direction whereas it is in the opposite direction in the case when the point is at the equatorial line of the electric dipole.
`\star` For both the cases (axial and equatorial), for distant point (r >>> 2a) the electric field, `E \prop \frac{1}{r^3}`
Question: Two point charges `5\mu C` and `- 5\mu C` are placed at 1 cm distance. Calculate the electric field intensity
(a) in axial line at a distance of 0.30 m. (b) in the equatorial line at a distance of 0.30 m.
Answer: (a) 3.33 `\times 10^4` N/C
Answer: (b) 1.67 `\times 10^4` N/C
Important Questions on Electric Dipole
Q. Which among the following statements best defines a dipole?
(1) Combination of two like and unequal charges positioned at the origin
(2) Combination of two unequal and like charges placed at the origin
(3) Combination of two equal and opposite charges separated by a small distance
(4) Combination of two unlike and unequal charges parted by a large distance
Answer: (3) Combination of two equal and opposite charges separated by a small distance
Q. What will be the total potential at a point P due to a dipole?
(1) Sum of potentials of the individual charges
(2) Difference of potentials of the individual charges
(3) Multiplication of potentials of the individual charges
(4) None of these
Answer: (2) Difference of potentials of the individual charges
Q. 3 C and -3 C are two equal charges separated by a distance of 4 cm, then calculate the dipole moment of a dipole.
(1) 0.12
(2) 0.14
(3) 0.16
(4) 0.18
Answer: (1) 0.12
Q. Which of the following phenomenon is experienced by the dipoles in an electric field?
(1) Interference
(2) Magnetisation
(3) Electromagnetism
(4) Polarisation
Answer: (4) Polarisation
Q. _____ can be calculated using the dipole moments.
(1) Intensity of electric field
(2) Patterns of polarization
(3) Susceptibility
(4) Strength of the dipole in the field
Answer: (2) Patterns of polarization
Q. On which among the following factors does dipole moment depend?
(1) Length only
(2) Length and charge of a dipole
(3) Dielectric constant and charge of the medium
(4) Charge only
Answer: (2) Length and charge of a dipole
Q. The nature of electric flux from the cube surface, if an electric dipole is placed inside a cube will be?
(1) The electric flux will be releasing out of the surface
(2) The electric flux will be coming into the surface
(3) There will be no flux at all
(4) None of these
Answer: (3) There will be no flux at all
Q. If a force F is acting on a point charge that is kept on the axis of an electric dipole, and if the distance of the point charge is tripled from the dipole, what will be the amount of force?
(1) 20F
(2) F/27
(3) F/25
(4) F/40
Answer: (2) F/27
Q. Which among the following is the dimensional formula of dipole moment?
(1) [L T I]
(2) [L1 T I2]
(3) [M2 L2 T I2]
(4) [L2 T2 I-2]
Answer: (1) [L T I]
Q. _____will act on an electric dipole if it is placed in a uniform electric field.
(1) Force only
(2) Both torque and force
(3) No force but torque
(4) None of these
Answer: (3) No force but torque
Practice Questions
1) What is an electric dipole?
2) What is the SI unit of dipole moment?
3) Give an example of an electric dipole.
4) Define 1 coulomb.
5) What is torque?
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