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  • (a) Derive an expression for the electric field E due to a dipole of length ‘2a’ at a point distant r from the centre of the dipole on the axial line. (b) Draw a graph of E versus r for r >> a. (c) If this dipole

(a) Derive an expression for the electric field E due to a dipole of length ‘2a’ at a point distant r from the centre of the dipole on the
axial line.
(b) Draw a graph of E versus r for r >> a.
(c) If this dipole were kept in a uniform external electric field E_{0}, diagrammatically represent the position of the dipole in stable and
unstable equilibrium and write the expressions for the torque acting on the dipole in both the cases.

 

 

 

 
 
 
 
 

Answers (1)

At point A electric field

E=\frac{kq}{(r-a)^{2}}-\frac{kq}{(r+a)^{2}}

where,

k=\frac{1}{4\pi \varepsilon _{o}}

= \frac{kq(4ar)}{(r^{2}-a^{2})^{2}}

= \frac{kr2(2aq)}{(r^{2}-a^{2})^{2}}

=\frac{2kPr}{\left ( r^{2}-a^{2} \right )^{2}}

for r>>a

E=\frac{2KP}{r^{3}}=\frac{1}{4\pi \varepsilon_{o} }\frac{2P}{r^{3}}

(b) r > > a

E\alpha \frac{1}{r^{3}}

(c) For stable equilibrium, P is parallel to E_{_{0}} and torque

\tau =\overrightarrow{P}\times E_{0}=0

For unstable equilibrium P is antiparallel to E_{_{0}} and

\tau =\overrightarrow{P}\times E_{0}=PE\sin (180)=0

Posted by

Safeer PP

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