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  • Obtain the expression for the electric field at a point on the equatorial line of an electric dipole.         <div sty

Obtain the expression for the electric field at a point on the equatorial line of an electric dipole.

 

 

 

 
 
 
 
 

Answers (1)

E_{+q} = \frac{1}{4\pi \varepsilon _{0}}\frac{q}{r^{2}+a^{2}}

E_{-q} = \frac{1}{4\pi \varepsilon _{0}}\frac{q}{r^{2}+a^{2}}

Components perpendicular to the dipole axis is cancelled.

The component along the dipole axis is added 

So, Total electric field is,

 E _{net}= -\left ( E_{+q}+E_{-q} \right )cos\theta

E = \frac{1}{4\pi \epsilon _{o}}.\frac{2q}{(r^{2}+a^{2})}\times \frac{a}{(r^{2}+a^{2})^{\frac{1}{2}}}

let q \times 2a=p

p is the dipole moment

then, E = \frac{1}{4\pi \varepsilon _{0}}\frac{p}{(r^{2}+a^{2})^{\frac{3}{2}}}

At a large distance ( r >>> a) this can be reduced 

E = \frac{1}{4\pi \varepsilon _{0}}\frac{P}{r^{3}}

Posted by

Safeer PP

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