Solved Examples of Electric Field of an Electric Dipole Calculations

📚 Quick Study Guide

🔍 Key Facts about Electric Dipoles:
• An electric dipole consists of two equal and opposite charges, $+q$ and $-q$, separated by a distance $d$.
💡 The dipole moment $\vec{p}$ is a vector pointing from the negative charge to the positive charge, with magnitude $p = qd$. 📝 The electric field due to a dipole is typically calculated at two important locations:
🧲 Along the axial line (the line extending along the dipole's length). 🧭 Along the equatorial line (the line perpendicular to the dipole's length, passing through the midpoint).

🧲 Electric Field Formulas

⚛️ Axial Electric Field (at a distance $r$ from the center of the dipole):
• $E_{axial} = \frac{1}{4\pi\epsilon_0} \frac{2pr}{(r^2 - (d/2)^2)^2}$
💡 If $r >> d$, then $E_{axial} \approx \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$ 🧪 Equatorial Electric Field (at a distance $r$ from the center of the dipole):
• $E_{equatorial} = \frac{1}{4\pi\epsilon_0} \frac{p}{(r^2 + (d/2)^2)^{3/2}}$
💡 If $r >> d$, then $E_{equatorial} \approx \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$

Practice Quiz

1. What is the direction of the electric dipole moment vector?
1. From the positive charge to the negative charge.
2. From the negative charge to the positive charge.
3. Perpendicular to the line joining the charges.
4. Along the direction of the electric field.


2. An electric dipole consists of charges $\pm 5 \times 10^{-6}$ C separated by 1 mm. What is its dipole moment?
1. $5 \times 10^{-9}$ C.m
2. $5 \times 10^{-8}$ C.m
3. $5 \times 10^{-7}$ C.m
4. $5 \times 10^{-6}$ C.m


3. The electric field due to a dipole falls off with distance $r$ as:
1. $\frac{1}{r}$
2. $\frac{1}{r^2}$
3. $\frac{1}{r^3}$
4. $\frac{1}{r^4}$


4. At a very large distance $r$ from an electric dipole, the axial electric field is proportional to:
1. $p/r$
2. $p/r^2$
3. $2p/r^3$
4. $p/r^4$


5. Compared to the axial electric field at a large distance $r$, the equatorial electric field at the same distance is:
1. Twice as strong.
2. Half as strong.
3. Equally strong.
4. Four times as strong.


6. If the charge on each side of a dipole is doubled, and the separation is halved, what happens to the dipole moment?
1. It remains the same.
2. It doubles.
3. It quadruples.
4. It halves.


7. What is the net charge of an electric dipole?
1. $q$
2. $-q$
3. $2q$
4. Zero