Question

Find electric field at any point on dipole seprated by a small distance 2a? Derive✌️

Answer 1

Final Answer :
$\frac{kp}{ {r}^{3} } \sqrt{1 + 3 { (\cos( \theta)})^{2} }$

This Electric field is in polar - Co ordinate at any general angle
$(r. \theta)$

Understanding:
1) Electric Field on the axis of a dipole is
$\frac{2kp}{ {r}^{3} }$
where p is dipole vector.

2) Electric field on the equatorial axis is
$\frac{ - kp}{ {r}^{3} }$

where p is dipole vector.

These Identities will be used in derivation.


Steps :
1) We will take any general point (r,/theta) .
2) We will find Electric field at point by taking components of dipole vector along and parallel to (r) vector.
3) For Along, r vector will use identity for axis Electric Field by dipole.
4) For Perpendicular to (r), we will use Identity for Equatorial Field by angle (r) .
5) Then, we will find
E(res) = √ ( E (p) ^2 + E(A)^2)
where
E(p) = Electric field perpendicular to (r) vector.
E(A) = Electric Field along (r) vector.


For Calculation see pic

Answer 2

Explanation:

Steps :

1) We will take any general point (r,/theta) .

2) We will find Electric field at point by taking components of dipole vector along and parallel to (r) vector.

3) For Along, r vector will use identity for axis Electric Field by dipole.

4) For Perpendicular to (r), we will use Identity for Equatorial Field by angle (r) .

5) Then, we will find

E(res) = √ ( E (p) ^2 + E(A)^2)

where

E(p) = Electric field perpendicular to (r) vector.

E(A) = Electric Field along (r) vector.

For Calculation see pic