Question

If \[{E_a}\]​ be the electric field strength of a short dipole at a point on its axial line and \[{E_e}\]​ that on the equatorial line at the same distance, then
A. \[{E_e} = 2{E_a}\]
B. \[{E_a} = 2{E_e}\]
C. \[{E_e} = {E_a}\]
D. None of the above

Answer 1

Hint:Here first of all we use the formula of the electric field at axial and equatorial points. After that, we compare both of them to get the required result.
The axial line is the line joining the centre of two charges which form an electric dipole. The equatorial line is perpendicular to the axial line which passes through the centre of the electric dipole.

Formula used Electric field at axial point is given as,
\[{E_a} = \dfrac{{2kp}}{{{r^3}}}\]
Electric field at equatorial point is given as,
\[{E_e} = \dfrac{{kp}}{{{r^3}}}\]

Complete step by step solution:
Given ​ electric field strength of a short dipole at a point on its axial line \[{E_a}\] and on the equatorial line \[{E_e}\] be at the same distance. As we know Electric field at axial point is:
\[{E_a} = \dfrac{{2kp}}{{{r^3}}}\]
As we know Electric field at equatorial point is:
\[{E_e} = \dfrac{{kp}}{{{r^3}}} \\ \]
Now to find the relation between the electric field at axial(\[{E_a}\]) point and electric field at equatorial point(\[{E_e}\]), divide both the equation
\[\dfrac{{{E_a}}}{{{E_e}}} = \dfrac{{2kp}}{{{r^3}}} \times \dfrac{{{r^3}}}{{kp}} \\ \]
\[\Rightarrow \dfrac{{{E_a}}}{{{E_e}}} = 2 \\ \]
\[\therefore {E_a} = 2{E_e}\]
Therefore the electric field strength at a point on its axial line is 2 times the electric field strength​ of that on the equatorial line at the same distance.

Hence option B is the correct answer.

Note:The electric field intensity is inversely proportional to the cube of the distance from the short dipole. The axial line can be defined as the line which is passing through the positive and negative charges. The point lying on that line is known as the axial point. An equatorial line can be defined as the perpendicular line to the line passing through the positive and negative charges. The point that lies on that line is known as the equatorial point.