Two short dipoles (A,B), A having charges and length and B having charges and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centre

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Solution

Q.
Two short dipoles (A,B), A having charges $\pm 2 μ C$ and length $1 cm$ and B having charges $\pm 4 μ C$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is ______ N/C. [2026]

1 $\frac{9}{16} \sqrt{2} \times 10^{4}$

2 $\frac{9}{16} \sqrt{2} \times 10^{5}$

3 $4.5 \sqrt{2} \times 10^{4}$

4 $9 \sqrt{2} \times 10^{4}$

Ans.
(1)

[IMAGE 198]

${\vec{E}}_{2} = - \frac{K P_{2}}{r^{3}}; {\vec{E}}_{1} = - \frac{2 K P_{1}}{r^{3}}$

$P_{1} = 2 \times 10^{- 6} \times 10^{- 2} = 2 \times 10^{- 8}$

$P_{2} = 4 \times 10^{- 6} \times 10^{- 2} = 4 \times 10^{- 8}$

${\vec{E}}_{net} = \frac{2 \times 9 \times 10^{9} \times 2 \times 10^{- 8}}{{(0.4)}^{3}} \hat{i} - \frac{9 \times 10^{9} \times 4 \times 10^{- 8}}{{(0.4)}^{3}} \hat{j}$

${\vec{E}}_{net} = \frac{9 \times 10^{9} \times 4 \times 10^{- 8}}{{(0.4)}^{3}} (\hat{i} - \hat{j})$

$| {\vec{E}}_{net} |$ $= \frac{9 \times 10^{4}}{16} \sqrt{2}$

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