Question

What is the ratio of electric fields at a given distance from an electric dipole at any point on its end-on side to that on its broad on side?

Answer 1

Explanation:

(1)E

=

4πϵ

0

1

×

(r

2

−a

2

)

2

2pr

(2)E

2

=

4πϵ

0

1

×

(r

2

+a

2

)

3/2

p

(ii) E

1

=2E

2

,E

1

:E

2

=2:1

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Answer 2

Answer:

The ratio of electric fields at a given distance from an electric dipole at any point on its end-on side to that on its broad on side is $2:1$.

Explanation:

Consider an electric dipole of two equal and opposite charges $-q$ and $+q$ separated by a distance $2l$, placed in a medium of dielectric constant $K$ at a point P of distance $r$ from an electric dipole.

When the point is along the axis of the dipole, the position is called axial position or end on position.

• The electric field intensity due to dipole at a point on end on position is

       $E_a=\dfrac{1}{4\pi \varepsilon_0K} \bigg(\dfrac{2pr}{(r^2-l^2)^{2} } \bigg)$

• For short electric dipole $r > > l$, so $l$ can be neglected.
• In air or vacuum, $K=1$.
• Then, $E_a=\dfrac{1}{4\pi \varepsilon_0} \bigg(\dfrac{2p}{r^3 } \bigg)$
• Where $p$ is the dipole moment of the electric dipole.

When the point is on a line perpendicular to the axis of the dipole, the position is called equatorial position or broad side on position.

• The electric field intensity due to dipole at a point on broad on side position is given by

       $E_q=\dfrac{1}{4\pi \varepsilon_0K} \bigg(\dfrac{p}{(r^2+l^2)^{3/2} } \bigg)$

• For  $r > > l$ and for $K=1$, the electric field intensity is

       $E_q=\dfrac{1}{4\pi \varepsilon_0} \bigg(\dfrac{p}{r^3 } \bigg)$

The ratio of two electric fields is at a given distance from an electric dipole at any point on its end-on side to that on its broad on side is

$\dfrac{E_a}{E_q} =\dfrac{ \dfrac{1}{4\pi \varepsilon_0} \bigg(\dfrac{2p}{r^3 } \bigg)}{\dfrac{1}{4\pi \varepsilon_0} \bigg(\dfrac{p}{r^3 } \bigg)}=\dfrac {2p}{p}}=\dfrac{2}{1}$

Therefore, the ratio of electric fields at a given distance from an electric dipole at any point on its end-on side to that on its broad on side is $2:1$.