Question

The ratio of electric fields on the axis and at equator of an electric dipole will be
A. 1:1
B. 2:1
C. 4:1
D. 1:4

Answer 1

Hint:Magnetic field strength is also called magnetic intensity or magnetic field intensity. Magnetic intensity can be calculated as the ratio of the strength of the magnetizing field to the permeability of free space. Be careful in order to find the electric field at the axis and at the equator of an electric dipole.

Formula used:
Magnitude of the intensity of electric field at a distance r on axial line is given as,
\[{E_a} = \dfrac{1}{{4\pi {\varepsilon _0}}} \times \dfrac{{2p}}{{{r^3}}}\]
Where p is electric dipole moment, \[{E_a}\] is the intensity of electric field on axial line, r is distance from dipole, k is coulomb’s constant, \[k = \dfrac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}N{m^2}\] and \[{\varepsilon _0}\] is permittivity.
Magnitude of the intensity of electric field at a distance r on equatorial line is given as,
\[{E_e} = \dfrac{1}{{4\pi {\varepsilon _0}}} \times \dfrac{p}{{{r^3}}}\]
Where p is the dipole moment, \[{E_e}\] is the intensity of the electric field on the equatorial line.

Complete step by step solution:
Given magnitude of intensity of electric field at a distance x on axial line is equal to magnitude of intensity of electric field at a distance y on equatorial line. As we know magnitude of the intensity of electric field at a distance x on axial line,
\[{E_a} = \dfrac{1}{{4\pi {\varepsilon _0}}} \times \dfrac{{2p}}{{{r^3}}}\]
Magnitude of the intensity of electric field at a distance y on equatorial line,
\[{E_e} = \dfrac{1}{{4\pi {\varepsilon _0}}} \times \dfrac{p}{{{r^3}}}\]

Now according to the question equating both the terms, we get
\[\dfrac{{{E_a}}}{{{E_e}}} = \dfrac{{k \times \dfrac{{2p}}{{{r^3}}}}}{{k \times \dfrac{p}{{{r^3}}}}}\]
\[where,{\rm{ }}k = \dfrac{1}{{4\pi {\varepsilon _0}}}\]
By arranging this
\[\dfrac{{{E_a}}}{{{E_e}}} = \dfrac{2}{1}\]
Therefore the ratio is, \[{E_a}:{E_e} = 2:1\]. Therefore the ratio of electric fields on the axis and at equator of an electric dipole will be

Hence option B is the correct answer.

Note: The magnetic intensity is how much the magnetic field can magnetize a substance. Also the magnetic intensity can be defined as the capability of the magnetic field to magnetize the substance. The intensity of magnetization is defined as the change in the magnetic moment per unit volume. The ratio gives the relation between two amounts of the same quantity showing how many times one amount is with the other.