Browse by Stream
QnA
Home
Search for Exam, Articles, Questions
QnA
get app
Go To Your Study Dashboard
  1. Home
  2. (a) Draw the equipotential surfaces due to an electric dipole. (b) Derive an expression for the electric field due to a dipole of dipole moment  at a poi
# School

(a) Draw the equipotential surfaces due to an electric dipole.
(b) Derive an expression for the electric field due to a dipole of dipole moment \vec{P} at a point on its perpendicular bisector.

 

Answers (1)
S safeer

a)

 

(b)

E=\frac{1}{4\pi \varepsilon _{o}}\frac{q}{r^{2}}

Hence, r=\sqrt{a^{2}+x^{2}}

electric due to positive charge

 \\E_{+}=\frac{1}{4\pi \varepsilon _{o}}\frac{q}{(a^{2}+x^{2})} and

electric due to negative charge

E_{-}=\frac{1}{4\pi \varepsilon _{o}}\frac{q}{a^{2}+x^{2}} 

From the figure, the sine components get mutually cancelled and cosine components can be added.

So,

E_{net}=E_{+}\cos \theta +E_{-}\cos \theta

Since due to the same magnitude

E_{net}=2E_{+}\cos \theta \; \; \; \; \; \; \; (1)

Now, \cos \theta =\frac{a}{\sqrt{a^{^{2}}+x^{2}}}

then,

E_{net}=2\frac{1}{4\pi \varepsilon _{o}}\frac{q}{a^{2}+x^{2}}\frac{a}{\sqrt{a^{2}+x^{2}}}

E_{net}=\frac{1}{4\pi \varepsilon _{o}}\frac{2qa}{(a^{2}+x^{2})^{3/2}}

The dipole moment, \vec{P}=2qa

Now, if x\gg a

E_{net}=\frac{1}{4\pi \varepsilon _{o}}\frac{P}{x^{3}}

Similar Questions

Related Chapters

Preparation Products

Knockout NEET May 2021 (One Month)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Foundation 2021 Class 9th Maths

Master Maths with "Foundation course for class 9th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
Start Now
 
Exams
Articles
Questions