Name: Electric Charges and Electric Fields: A Review
Uploaded: 2019-07-19
Duration: 6 min 41 s
Description: In this video, we are going to review the electric charges, the law of charge, conservation of charges and electric field in detail. Watch this to learn more.

Question

What is meant by electric dipole and its dipole moment? Obtain an expression for an electric field due to an electric dipole at a point on the perpendicular bisector of the dipole.

Accepted Answer

Electric dipole :- When two point charges of equal magnitude and opposite in nature are separated by small distance then this arrangement is called an electric dipole.

The separation between two charges is represented by $2 l$

Which is called the dipole length.

Electric dipole moment :- The product of magnitude of either charge and the dipole length gives the measurement of magnitude of dipole

mathematically $P = q \times 2 l$

It is a vector physical quantity directed from $- q$ Charge to $+ q$ Charge and in vector form it is represented as $\vec{p} = q \times \vec{2 l}$

$S . I$ .unit = Coulomb's metre $(C-m)$

Dimensional formula $= [ATL]$ or $[ITL]$

Electric field due to an electric dipole at a point on the perpendicular bisector of the dipole:

Where $E_{1}$ and $E_{2}$ is the Electric Field Intensity at M due to $- q$ and $+ q$ charges respectively. Using coulomb's law:

$| \vec{E_{1}} | = \frac{1}{4 π ϵ_{0}} . \frac{q}{r^{2} + a^{2}}$

$| \vec{E_{2}} | = \frac{1}{4 π ϵ_{0}} . \frac{q}{r^{2} + a^{2}}$

So $\vec{| E_{1}} | = \vec{| E_{2}} | = \vec{| E} |$

$\vec{| E} | = 2 \vec{| E_{1}} | \cos (θ)$

$= \frac{2}{4 π ϵ_{0}} . \frac{q}{(r^{2} + a^{2})} \cos (θ)$

$= \frac{2}{4 π ϵ_{0}} . \frac{q}{(r^{2} + a^{2})} . \frac{a}{\sqrt{(r^{2} + a^{2})}}$

$= \frac{2}{4 π ϵ_{0}} . \frac{q a}{{(r^{2} + a^{2})}^{3 / 2}}$

Using $P = q (2 a)$

$∴ \vec{E} = \frac{- \vec{P}}{4 π ϵ_{0} {(r^{2} + a^{2})}^{3 / 2}}$

if $r > > a$ (special case)
Then, ${\vec{E}}_{n e t} = \frac{- K \vec{P}}{r^{3}} = \frac{- \vec{P}}{4 π ϵ_{0} r^{3}}$ (This is the value of $E_{n e t}$ when the dipole is placed in the vacuum.)

What is meant by electric dipole and its dipole moment? Obtain an expression for an electric field due to an electric dipole at a point on the perpendicular bisector of the dipole.

Important Questions on Electric Charges and Fields

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