field using dipole

[rigid eagle]

can some1 tell me how to get the answer with and without using dipole

[fossil owl]

<@&1227987967939838003>

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[rigid eagle]

i tried without dipole and using my imagination i was able to figure out net field should be 4*field due to one charge * sinalpha
(alpha mentioned in fig)

[tawny vine]

take out the feild from each charge and get a vector sum

it should give the ans

[rigid eagle]

i got pretty much the same ans but was missing 1/root2

[rigid eagle]

it indeed will but that vector sum itself is bothersome

[tawny vine]

nah it wont be

dipole here will make things more complicated

[raven pendant]

$$\frac{pK}{\sqrt{2}x^3}\left(\hat{z}-\hat{y}+\hat{z}+\hat{y}\right)$$

[chrome marten]

Opt

[raven pendant]

That's what I got.

Try simplifying, i might have made a mistake

[rigid eagle]

yep this is correct

how did u get this

[raven pendant]

It's along equatorial plane of both dipoles na?

[rigid eagle]

i couldnt visualise using dipole

[raven pendant]

$$-\frac{\vec{p}K}{r^3}$$

[chrome marten]

Opt

[raven pendant]

Diagonals are also dipoles

Use those

[rigid eagle]

yeah i got that part

there will be two components of field due to dipole

[raven pendant]

Yeah, the two fields are along z-y, and z+y (divided by √2 to make them unit vectors)

The p vectors are opposite to those vectors I just wrote.

I flipped them in my head and typed it.

[rigid eagle]

how did u fig out the dirn part

[raven pendant]

+q to -q

For field that is. Dipole moment is always - to +

[rigid eagle]

the dipole in red gives z-y or z+y

[raven pendant]

z-y

[rigid eagle]

i am thinking x+z

x-z

wait a min angle between p vector and r vector is 90 so radial component cancels only the other one remains

[raven pendant]

Look at the axes

They've given the axes already

[raven pendant]

@rigid eagle got it?

[rigid eagle]

no not really

[eternal quail]

dipoles would have effects in their axes, not in one perpendicular to them.
Any reason you have taken the axis to be x?

https://www.khanacademy.org/science/electromagnetism/x4352f0cb3cc997f5:how-a-microwave-oven-works/x4352f0cb3cc997f5:what-are-electric-dipoles-and-how-do-they-behave-in-electric-fields/v/electric-dipoles-dipole-moments

[raven pendant]

They have effects along axis perpendicular to them as well

[eternal quail]

wont that get cancelled out here?

[raven pendant]

Oh you mean the field along perpendicular

Those don't exist

Mb mb

Yeah field is always parallel/antiparallel to dipole moment

[eternal quail]

haan matlab they are planar, is what i recall

[rigid eagle]

for the marked dipole i am imagining a plane similar to xy plane but tilted 45 degs from y axis inwards

now angle between p vector and r vector ( from centere of dipole i.e origin to point M) is 0
so field along r vector becomes zero
field perpendicualr to r vector is kp/r^3