The electric field of a dipole at a point on its equatorial plane is found by adding the fields \(\vec E_{+q}\) and \(\vec E_{-q}\) of its two charges. These two fields are equal in magnitude. Which of the following is correct about their sum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The components normal to the dipole axis cancel, so the total field is opposite to the dipole moment.
The field of \( +q \) points away from \( +q \), and the field of \( -q \) points towards \( -q \). The dipole moment \( \vec p \) points from \( -q \) to \( +q \).
Option (1) The components along the dipole axis cancel, so the total field is normal to the axis. — Incorrect. Both fields have a part along the axis that points from the \( +q \) side towards the \( -q \) side. These parts add, so they cannot cancel.
Option (2) The components normal to the dipole axis cancel, so the total field is along the dipole moment. — Incorrect. The parts along the axis point from the \( +q \) side towards the \( -q \) side. This is opposite to \( \vec p \), which points from \( -q \) to \( +q \).
Option (3) The components normal to the dipole axis cancel, so the total field is opposite to the dipole moment. — Correct. The parts normal to the axis are equal and opposite, so they cancel. The parts along the axis add. The total field points from the \( +q \) side towards the \( -q \) side, opposite to \( \vec p \).
Option (4) The two fields are opposite to each other, so the total field is zero. — Incorrect. The two fields do not lie along one line. Their parts along the axis add, so the total field is not zero.
NCERT (2026-27):
The field of an electric dipole – “… Clearly, the components normal to the dipole axis cancel away. The components along the dipole axis add up. The total electric field is opposite to p̂. …”