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Four point charges +q,+q,+q and -q are p...

Four point charges `+q,+q,+q` and `-q` are placed at the four comers of a square, length of each side of which is a.
Find the magnitude of the intensity of the electric field at the centre of the square.

Text Solution

Verified by Experts

The point of intersection O of the diagonals is equidistant from four charges.
`:.OA=OB=OC=OD=a/(sqrt(2))`
Intensities of electric field at O due to the charges at A and C balance each other, because the two fields are equal and opposite.
Intensity at O due to the charge aet `B=q/((a//sqrt(2))^(2))`, along `vec(OD)`
Intensity at O due to the charge at `D=q/((a//sqrt(2)^(2))`, along `vec(OD)`

Resultant intensity at O
`=q/((a//sqrt(2))^(2))+q/((a//sqrt(2))^(2))=(2q)/(a^(2))+(2q)/(a^(2))=(4q)/(a^(2))`, along `vec(OD)`
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