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An electric dipole lies along the z-axis with its mid-point at the origin. The electric field at an axial point at a distance z from the origin is E(z), and at an equatorial point at a distance y from the origin it is E(y). If z = y 2a (the length of the dipole), then (E(z))/(E(y)) = _____.

Asked in GUJCET 2007 · Dipole moment and dipole field

• (1) 1
• (2) 4
• (3) 3
• (4) 2

Step-by-step solution

Why the other options are wrong

• (1) This treats the two fields as equal. Both fall off as 1/(r³), but the axial field carries a factor 2 that the equatorial field does not.
• (2) 4 would need an axial field of (4kp)/(r³). The axial field is (2kp)/(r³) against (kp)/(r³) on the equator, so the ratio is 2; 4 is that ratio squared.
• (3) No single slip gives 3. The general dipole field has magnitude (kp)/(r³)√3 cos²θ+1, which is (2kp)/(r³) on the axis and (kp)/(r³) on the equator; the 3 inside the root is not the ratio.

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