A dipole is placed at origin of coordinate system as shown in figure, find the electric field at point $P (0, y)$ :

\frac{k P}{y^{3}} (-^i - 2^j)

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\frac{k P}{y^{3}} (-^i + 2^j)

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\frac{k P}{\sqrt{2} y^{3}} (-^i - 2^j)

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\frac{k P}{\sqrt{2} y^{3}} (-^i + 2^j)

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Solution

The correct option is C $\frac{k P}{\sqrt{2} y^{3}} (-^i - 2^j)$
The general expression of electric field due to dipole, $E = \frac{k}{r^{3}} [3 (\to p .^r)^r - \to p]$ where $p =$ dipole moment.
here, $p = P cos 45^i - P s i n 45^j = \frac{P}{\sqrt{2}} (^i -^j), r = y,^r =^j$
$\to p .^r = \frac{P}{\sqrt{2}} (^i -^j) .^j = - \frac{P}{\sqrt{2}}$
therefore, $E = \frac{k P}{\sqrt{2} y^{3}} [- 3^j -^i +^j] = \frac{k P}{\sqrt{2} y^{3}} [-^i - 2^j]$

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A dipole is placed at origin of coordinate system as shown in figure, find the electric field at point P(0,y):

The correct option is C kP√2y3(−^i−2^j)The general expression of electric field due to dipole,E=kr3[3(→p.^r)^r−→p] where p= dipole moment.here, p=Pcos45^i−Psin45^j=P√2(^i−^j),r=y,^r=^j→p.^r=P√2(^i−^j).^j=−P√2therefore, E=kP√2y3[−3^j−^i+^j]=kP√2y3[−^i−2^j]

A dipole is placed at origin of coordinate system as shown in figure, find the electric field at point $P (0, y)$ :