Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Derive an expression for the electric field at a point on the axis of an electric dipole of dipole moment . Also, write its expression when the distance <img alt="r

Derive an expression for the electric field at a point on the axis of an electric dipole of dipole moment \vec{p} . Also, write its expression when the distance r> > the length ‘a’ of the dipole.

 

 

 
 
 
 
 

Answers (1)

Let us consider on electric dipole of length 2a. Now, consider a point 'p' along the dipole whose distance from the centre 'O' is 'r' thus,



Electric field produce at p due to -q charge 

E_{-q}=\frac{q}{4\pi \epsilon _{0}(r+a)^{2}}

Electric field produce at p due to +q charge 

E_{+q}=\frac{q}{4\pi \epsilon _{0}(r-a)^{2}}

therefore, the total field at p, will be;-

E=E_{-0}-E_{+}

On equating the values, we get

  E=\frac{q}{4\pi \epsilon _{0}(r-a)^{2}}-\frac{q}{4\pi \epsilon _{0}(r+a)^{2}}

E=\frac{q}{4\pi \epsilon _{0}}\left [ \frac{1}{(r-a)^{2}}-\frac{1}{(r+a)^{2}} \right ]

E=\frac{q}{4\pi \epsilon _{0}}\left [ \frac{(r+a)^{2}-(r-a)^{2}}{(r-a)^{2}(r+a)^{2}} \right ]

E=\frac{q}{4\pi \epsilon _{0}}\left [ \frac{r^{2}+a^{2}+2ra-r^{2}-a^{2}+2ra}{(r^{2}-a^{2})^{2}} \right ]

E=\frac{q}{4\pi \epsilon _{0}}\frac{2\times 2ra}{(r^{2}-a2)^{2}}  OR \frac{1}{4\pi \epsilon _{0}}\frac{2pr}{(r^{2}-a^{2})^{2}}

For, r> > a

then, 

\therefore E=\frac{1}{4\pi \epsilon _{0}}\frac{2p}{r^{3}}

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Result 2025 Live: UK Board 10th, 12th results tomorrow; AP SSC, TS Inter, UP, CBSE updates
anam-khan

When will CBSE Class 12 results 2025 be declared? Last two years' trends
anam-khan

CBSE Class 10, 12 board exams 2025 from April 7 to 11 for sports students

Latest Question