Question

E1 and E2 respectively denote the magnitude of the electric field intensity at two point on the axial line at distances r and 2r from the mid points of the dipole the ratio E1:E2

Answer 1

Answer:

(1)E

1

=

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

Explanation:

please follow me

Answer 2

Given:

E1 and E2 respectively denote the magnitude of the electric field intensity at two point on the axial line at distances r and 2r from the mid points of the dipole.

To find:

E1 : E2 ratio.

Calculation:

General expression of electrostatic field intensity at axial position of a short dipole at a distance d is given as:

$\boxed{ \bold{ \large{E = \dfrac{2kp}{ {d}^{3} } }}}$

Here "k" is Coulomb's Constant , "p" is Dipole moment .

So , in 1st case:

$\sf{ \therefore \: E1 = \dfrac{2kp}{ {r}^{3} } }$

So, in 2nd case:

$\sf{ \therefore \: E2 = \dfrac{2kp}{ {(2r)}^{3} } }$

$\sf{ = > \: E2 = \dfrac{2kp}{8 {r}^{3} } }$

$\sf{ = > \: E2 = \dfrac{1}{8} \times \dfrac{2kp}{ {r}^{3} } }$

So, required ratio:

$\sf{ \therefore \: E1 : E2 = 1 : \dfrac{1}{8} }$

$\boxed{ \bold{ \large{ = > E1 : E2 = 8 : 1}}}$

HOPE IT HELPS.