An electric dipole coincides on Z-axis and its midpoint is on origin of the coordinate system. The electric field at an axial point at a distance z from origin is E(z) and electric field at an equatorial point at a distance y from origin is E( y) . Here z = y a, so | ( E (z) / E(y)) | = ...

Question

An electric dipole coincides on Z-axis and its midpoint is on origin of the coordinate system. The electric field at an axial point at a distance z from origin is E(z) and electric field at an equatorial point at a distance y from origin is E( y) . Here z = y > a, so | ( E (z) / E(y)) | = ... (A) 1 (B) 4 (C) 3 (D) 2

Tardigrade Admin · Accepted Answer

The magnitude of electric field at an axial point M at a distance z from the origin is given by

∣ E_{z} ∣ = \frac{1}{4 π ε _{0}} . \frac{2 p z}{( z ^{2} - a ^{2} ) ^{2}}

For

z >> a, ∣ E_{z} ∣ = \frac{2 p}{4 π ε _{0} z ^{3}}

and, magnitude of electric field at a equatorial point N at a distance y from origin (0, 0) is given by

∣ E_{y} ∣ = \frac{p}{4 π ε _{0} ( y ^{2} + a ^{2} ) ^{3/2}}

For

y >> a, ∣ E_{y} ∣ = \frac{1}{4 π ε _{0}} . \frac{p}{y ^{3}}

For

z = y >> a

∴ ∣ ∣ \frac{E _{(z)}}{E _{(y)}} ∣ ∣ = 2