Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
before looking at what the question says ,
let's have some general information related to the topic of the question !
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[tex]\implies \: [/tex] Electric field refers to the force generated by a nearby charge in the surroundings.
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[tex]\implies \: [/tex] Mathematically ,
Electric field = [tex]\frac{Kq}{r^{2}} \\[/tex]
where ,
K = coulomb's constant
q = magnitude of charge
r = distance between the opposite terminals
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[tex]\implies \: [/tex] Dipole moment , P = 2qd
where ,
q = magnitude of charges
d = distance between the charges
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[tex]\implies \: [/tex] positive charge tends to throw the field away from it while negative charge tends to pull the field towards it !
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seems like enough of information , so now let's look at the derivation !
refer the attachments in order to see the derivation !
Final answer -
[tex]\bold\pink{E = \frac{2kp}{(x {}^{2} - d {}^{2} ) {}^{2} } } \\ [/tex]
while , for a short dipole
[tex]\bold\pink{E = \frac{2pk}{x {}^{3} }} \\ [/tex]
hope helpful :D
