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` (maybe 2r or 2a).
`star` The midpoint between the two charges is called the center of the electric dipole.
`star` The line joining these charges is called the axial line.
`star` The line perpendicular to the axial line and passing through the center is called the 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.
Torque on a Dipole in Uniform Electric Field
Let there be an electric dipole, the distance between the two charges (+q and - q) is 2a. This electric dipole is placed in a uniform electric field with the angle of `\theta`. The force acting on its positive charge (F = +qE) is in the direction of the electric field. and the force on the negative charge (F = - qE) acts in the opposite direction to the electric field. These forces are equal in magnitude but opposite in direction, due to which torque is produced on the electric dipole.
Torque = force `\times` perpendicular distance between both forces
`\tau` = F `\times` (AC)
`\tau` = qE `\times` (2a `sin\theta`)
`\tau` = q(2a) E `sin\theta`
`\tau` = p E `sin\theta` `{\because p = q (2a)}`
`\vec\tau` = `\vec p \times \vec E`
`\star` Direction of electric dipole moment p is along -q to +q.
`\star` Direction of Torque is along in the direction of `\vec p \times \vec E`.
`\star` We can find the direction of torque with the help of the right-hand thumb rule.
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| Torque on a Dipole |
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| Stable Equilibrium |
(i) If `\theta = 0^\circ` than `sin\theta = sin 0 = 0`
`\vec\tau` = `\vec p \times \vec E`
`\tau` = p E `sin\theta`
`\tau` = p E `sin 0`
`\tau` = p E (0)
`\tau` = 0
This is a stable Equilibrium.
(ii) If `\theta = 180^\circ` than `sin\theta = sin 180 = 0`
`\vec\tau` = `\vec p \times \vec E`
`\tau` = p E `sin\theta`
`\tau` = p E `sin 180`
`\tau` = p E (0)
`\tau` = 0
This is an unstable Equilibrium.
Questions and Answer
1. What is the midpoint between two charges of equal magnitude and opposite nature called? (Answer: Center of electric dipole)
2. What is the line joining the two charges called? (Answer: Axial line)
3. What is the line perpendicular to the axial line and passing through the center called? (Answer: Equatorial line)
4. Define the dipole moment in terms of charge and distance between them. (Answer: Dipole moment = charge × distance)
5. What is the unit of electric dipole moment? (Answer: Coulomb × meter)
6. Provide the dimensions of electric dipole moment. (Answer: `[M^0L^1T^1A^1`])
7. Give an example of a substance that exhibits electric dipole. (Answer: HCl, NaCl, etc.)
8. Calculate the electric dipole moment of a NaCl molecule if the distance between Na+ and `Cl^-` ions is 1.28 Ã…. (Answer: `2048 \times 10^{-29}` C·m)
9. State the expression for torque on a dipole in a uniform electric field. (Answer: Torque = p × E × sinθ)
10. What is the direction of torque in relation to the direction of the electric dipole moment and the electric field? (Answer: Along the direction of p × E)
11. Two Charges `\pm 1000 \mu C` are at distance 2 mm, form an electric dipole. This electric dipole is placed in a uniform electric field of `15 \times 10^4 N/C` at an angle `30^\circ`. Calculate the torque acting on the dipole. (Answer 15 `\times 10^{-2} Nm`)
Torque o a Dipole in Uniform Electric Field MCQs
1. The midpoint between two charges of an electric dipole is called:
(a) Equatorial line
(b) Axial line
(c) Center of electric dipole
(d) None of the above
2. The line joining the two charges of an electric dipole is called:
(a) Equatorial line
(b) Axial line
(c) Center of electric dipole
(d) None of the above
3. The line perpendicular to the axial line and passing through the center of an electric dipole is called:
(a) Equatorial line
(b) Axial line
(c) Center of electric dipole
(d) None of the above
4. The product of the charge and the distance between them in an electric dipole is called:
(a) Electric dipole moment
(b) Electric field
(c) Electric potential
(d) Electric force
5. The unit of electric dipole moment is:
(a) Coulomb
(b) Meter
(c) Coulomb per meter
(d) Coulomb-meter
6. The dimensions of electric dipole moment are:
(a) `[M^0L^0T^0A^0]`
(b) `[M^0L^1T^1A^1]`
(c) `[M^1L^1T^-2A^-2]`
(d) `[M^1L^0T^-2A^-1]`
7. Examples of electric dipoles include:
(a) H2O, CO2
(b) NaCl, HCl
(c) CH4, NH3
(d) O2, N2
8. Torque on an electric dipole in a uniform electric field is given by:
(a) `\tau = pE \sin\theta`
(b) `\tau = pE \cos\theta`
(c) `\tau = p/E \sin\theta`
(d) `\tau = p/E \cos\theta`
9. The direction of the electric dipole moment is along:
(a) The positive charge to the negative charge
(b) The negative charge to the positive charge
(c) The equatorial line
(d) The axial line
10. The direction of torque on an electric dipole is given by:
(a) Along the electric field
(b) Opposite to the electric field
(c) Along the axial line
(d) Perpendicular to the electric dipole moment
Answers:
1. (c) Center of electric dipole
2. (b) Axial line
3. (a) Equatorial line
4. (a) Electric dipole moment
5. (d) Coulomb-meter
6. (b) `[M^0L^1T^1A^1]`
7. (b) NaCl, HCl
8. (a) `\tau = pE \sin\theta`
9. (b) The negative charge to the positive charge
10. (d) Perpendicular to the electric dipole moment
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