Two shorts dipoles $$(A, B)$$, $$A$$ having charges $$\pm 2\mu C$$ and length 1 cm and $$B$$ having charges $$\pm 4\mu C$$ 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.

Distance from each dipole center to P:

r=40 cm=0.4m

Dipole moments:

$$p_A=(2\times10^{-6})(10^{-2})=2\times10^{-8}$$

$$p_B=(4\times10^{-6})(10^{-2})=4\times10^{-8}$$

For dipole A (axial point),

$$E_A=\frac{1}{4\pi\epsilon_0}\frac{2p_A}{r^3}$$

$$=9\times10^9\cdot\frac{2(2\times10^{-8})}{(0.4)^3}$$

=5625

For dipole B (equatorial point),

$$E_B=\frac{1}{4\pi\epsilon_0}\frac{p_B}{r^3}$$

=5625

So magnitudes are equal.

Directions:

• $$E_A$$​ is horizontal
• $$E_B$$​ is vertical

They are perpendicular.

Hence resultant:

$$E=\sqrt{E_A^2+E_B^2}$$

$$=5625\sqrt{2}$$

$$=\frac{9}{16}\times10^4\sqrt{2}$$