Electric Dipole: Comprehensive NEET Physics Notes

1. Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. The dipole is characterized by a dipole moment ($p$), which is a vector quantity pointing from the negative charge to the positive charge.

1.1 Dipole Moment

The dipole moment ($p$) is given by the product of the magnitude of either charge ($q$) and the separation distance between the charges ($2a$):

$p=q\times 2a$

• Unit: Coulomb-meter (C·m)
• Direction: From the negative charge to the positive charge

The dipole moment is critical as it determines the behavior of the dipole in an electric field. A larger dipole moment signifies stronger interaction with external electric fields.

1.2 Electric Field Due to a Dipole

The electric field created by an electric dipole is distinct from that of a single charge. It depends on both the distance from the dipole and the angle relative to the dipole axis. The field strength decreases more rapidly than that of a point charge as distance increases.

1.2.1 Electric Field at Axial Position

The axial position lies along the line connecting the two charges. The electric field at an axial point, located at a distance $r$ from the center of the dipole, is:

$E_{\text{axial}}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{2p}{r^3}$

1.2.2 Electric Field at Equatorial Position

The equatorial position is perpendicular to the line connecting the charges. The electric field at an equatorial point, located at a distance $r$ from the center of the dipole, is:

$E_{\text{equatorial}}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{p}{r^3}$

At the equatorial position, the electric field is weaker than at the axial position and directed opposite to the dipole moment.

Did You Know?

The electric field of a dipole decreases as $1/r^3$, while the field of a single charge decreases as$1/r^3$. This means dipoles significantly influence the field only at short distances.

2. Potential Due to an Electric Dipole

The electric potential at a point due to an electric dipole is the sum of the potentials created by each charge. For a point at a distance $r$ from the center of the dipole and at an angle $\theta$ relative to the dipole axis, the potential is:

$V=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{p\cos \theta }{r^2}$

Where:

• $p$ is the dipole moment
• $r$ is the distance from the center of the dipole
• $\theta$ is the angle between the dipole axis and the line joining the center of the dipole to the point

At points along the axial line ($\theta =0$), the potential is maximized, while at points along the equatorial line ($\theta =90^{\circ }$), the potential is zero.

Common Misconception

Students often mistakenly assume the dipole moment points from positive to negative charge. Remember, the dipole moment points from the negative to the positive charge.

3. Electric Dipole in a Uniform Electric Field

When an electric dipole is placed in a uniform electric field ($E$), it experiences a torque ($\tau$) but no net translational force. The torque tends to align the dipole with the electric field. The torque ($\tau$) is given by:

$\tau =p\times E=pE\sin \theta$

Where:

• $p$ is the dipole moment
• $E$ is the external electric field
• $\theta$ is the angle between $p$ and $E$

The potential energy ($U$) of the dipole in the electric field is:

$U=-pE\cos \theta$

When $\theta =0$, the dipole is aligned with the field, and the potential energy is minimized ($U_{\text{min}}=-pE$). When $\theta =180^{\circ }$, the potential energy is maximized ($U_{\text{max}}=pE$).

NEET Tip:

Questions related to the torque and potential energy of a dipole in an electric field frequently appear in NEET. Ensure you understand how the dipole behaves in different orientations relative to the electric field.

4. Graphical Representation

A useful way to understand the electric field and potential due to a dipole is through graphs and diagrams:

• Field lines: Field lines start from the positive charge and end at the negative charge.
• Equipotential surfaces: Around a dipole, equipotential surfaces are elliptical in shape.

Suggested Diagram: Show a dipole with its field lines and equipotential surfaces. Highlight the difference in field strength along the axial and equatorial positions.

Quick Recap

• Electric Dipole: Two equal and opposite charges separated by a small distance.
• Dipole Moment:$p=q\times 2a$, direction from negative to positive charge.
• Electric Field: Axial field $E_{\text{axial}}=\frac{2p}{r^3}$, Equatorial field $E_{\text{equatorial}}=\frac{p}{r^3}$.
• Potential: $V=\frac{p\cos \theta }{r^2}$, zero at the equatorial plane.
• Torque in a Field: $\tau =pE\sin \theta$.
• Potential Energy in a Field: $U=-pE\cos \theta$.

Practice Questions

1. Find the dipole moment of a system consisting of two charges $+5\mu C$ and $-5\mu C$ separated by a distance of $2cm$.
2. • Solution: $p=q\times 2a=5\times 10^{-6}\times 0.02=1\times 10^{-7}C\cdot m$
2. Calculate the electric field at a point $5cm$ away from the center of a dipole along its axial line. The dipole moment is $2\times 10^{-6}C\cdot m$.
3. • Solution: $E_{\text{axial}}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{2p}{r^3}=9\times 10^9\times$