A system has two charges, \( q_A = 5 \times 10^{-7}\,\mathrm{C} \) and \( q_B = -5 \times 10^{-7}\,\mathrm{C} \), located at points A: (0, 0, -10 cm) and B: (0, 0, +10 cm), respectively. Which of the following are true?
(A) the electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^{6}\,\mathrm{NC^{-1}} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment (p)= \( 5 \times 10^{-8} \) C-m
(D) direction of the dipole moment is along the negative z-axis
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (D) only
The two charges form an electric dipole on the \( z \)-axis: \( +q \) at \( z = -10\,\mathrm{cm} \) and \( -q \) at \( z = +10\,\mathrm{cm} \), with \( q = 5\times10^{-7}\,\mathrm{C} \) and separation \( 2a = 0.2\,\mathrm{m} \). The field of a point charge points away from a positive charge and towards a negative one.
\( \displaystyle kq = 9\times10^{9} \times 5\times10^{-7} = 4.5\times10^{3}\,\mathrm{N\,m^2\,C^{-1}} \)
(A) the electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^{6}\,\mathrm{NC^{-1}} \) — Correct. The point is 5 cm from \( q_A \) and 25 cm from \( q_B \). The field of \( q_A \) points away from A, along \( -z \); the field of \( q_B \) points towards B, along \( +z \).
\( \displaystyle E = \frac{kq}{(0.05)^{2}} - \frac{kq}{(0.25)^{2}} = 4.5\times10^{3}\,(400 - 16) = 1.728\times10^{6} \approx 1.73\times10^{6}\,\mathrm{N\,C^{-1}} \)
(B) Electric field intensity is zero at origin (0, 0, 0) — Incorrect. At the origin both fields point along \( +z \) (away from A and towards B), so they add and the field is not zero.
(C) dipole moment (p)= \( 5 \times 10^{-8} \) C-m — Incorrect. The dipole moment is the charge times the separation.
\( \displaystyle p = q\,(2a) = 5\times10^{-7} \times 0.2 = 1\times10^{-7}\,\mathrm{C\,m} \)
(D) direction of the dipole moment is along the negative z-axis — Correct. The dipole moment points from the negative charge to the positive charge, here from B (\( z = +10\,\mathrm{cm} \)) to A (\( z = -10\,\mathrm{cm} \)), that is, along \( -z \).
NCERT (2026-27):
The Field of an Electric Dipole – “… The dipole moment vector \( \mathbf{p} \) of an electric dipole is defined by
\( \displaystyle \mathbf{p} = q \times 2a\,\hat{\mathbf{p}} \qquad (1.19) \)
that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) and the direction is along the line from –q to q.”