Q.
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 \, \bigg | \frac{ E_{ (z) }}{ E_{(y)}} \bigg | = $ ...
Gujarat CETGujarat CET 2007Electric Charges and Fields
Solution:
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 \pi \varepsilon_0 } . \frac{ 2 \, pz}{ (z^2 - a^2 )^2 } $
For $z >> a, | E_z | = \frac{ 2p}{ 4 \pi \varepsilon_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 \pi \varepsilon_0 ( y^2 + a^2 )^{3/2}}$
For $y >> a, | E_y | = \frac{ 1}{ 4 \pi \varepsilon_0 }. \frac{ p}{ y^3 } $
For $z = y >> a$
$\therefore \:\: \bigg| \frac{ E_{ (z) }}{ E_{(y)}} \bigg | = 2 $
