Answer to Question #91660 in Electric Circuits for Abhay

Question #91660
Electric field strength due to dipole of moment p at a distant point r along the axis of the dipole is
1
Expert's answer
2019-07-15T09:25:10-0400


Electric field strength in point A

E=q4πϵ0(1r221r12)E=\frac{q}{4\pi \epsilon_0}\left(\frac{1}{r_2^2}-\frac{1}{r_1^2}\right)

We may apply the mean value theorem

E=q4πϵ0ddr(1r2)r=ξ(r2r1)=14πϵ02pξ3E=\frac{q}{4\pi \epsilon_0}\frac{d}{dr} \left(\frac{1}{r^2} \right) \bigg|_{r=\xi}(r_2-r_1)=\frac{1}{4\pi \epsilon_0}\frac{2p}{\xi^3}

where

ξ[r2,r1]\xi \in [r_2,r_1]

Dipole is a point particle, hence

ξ=r\xi=r

where r is a distance between dipole and point A.

So the electric field strength due to dipole of moment p at a distant point r along the axis of the dipole is

E=14πϵ02pr3E=\frac{1}{4\pi \epsilon_0}\frac{2p}{r^3}

or in vector form

E=14πϵ02pr3\vec E=\frac{1}{4\pi \epsilon_0}\frac{2\vec p}{r^3}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment