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Question

Two short electric dipoles of moment P and 27P are placed as shown below. If at the point O the electric field is zero between the dipoles, then the distance of the point O from the centre of first dipole is


A
2 cm
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B
4 cm
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C
6 cm
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D
8 cm
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Solution

The correct option is A 2 cm
Let the electric field at point O due to dipole (1) be E1 and due to dipole (2) be E2.

At O,
E1E2=0E1=E2

Let point O be x distance away from dipole (1). Then it will be (8x) distance away from dipole (2)

For a short dipole, electric field at axial line of dipole is given by
|E|=2k|p|x3

for electric dipole (1),

E1=2kPx3

and for electric dipole (2),

E2=2k×27P(8x)3

Since, E1=E2

2kPx3=2k×27P(8x)3

1x3=27(8x)3

(8x)3=33×x3

8x=3x

x=2 cm

So, option (a) is correct.

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