Question

E1 is electric field on the axis of a small electric dipole at a distance r and E2 is at same distance r but an angle 60 degree from the dipole. then find ratio of e1 and e2

Answer 1

Explanation:

answer in the attachment

Answer 2

The ratio

$E_1:E_2=4:\sqrt 7$

Explanation:

Electric field on the axis of a small electric dipole at distance r=$E_1=\frac{2kP}{r^3}$

Electric field at distance r and makes an angle $\theta$ with dipole

$E=\frac{kP}{r^3}\sqrt{1+3cos^2\theta}$

Electric field at distance r and makes an angle 60 degree with dipole then

$\theta=60^{\circ}$

Using the formula

$E_2=\frac{kP}{r^3}\sqrt{1+3cos^260^{\circ}}$

$cos60^{\circ}=\frac{1}{2}$

Substitute the values then we get

$E_2=\frac{kP}{r^3}\sqrt{1+3(\frac{1}{2})^2}$

$E_2=\frac{kP}{r^3}(\sqrt{\frac{4+3}{4}})$

$E_2=\frac{kP}{r^3}(\frac{\sqrt 7}{2})$

$E_1/E_2=\frac{\frac{2kP}{r^3}}{\frac{kp\sqrt 7}{2r^3}}$

$E_1/E_2=\frac{4}{\sqrt 7}$

$E_1:E_2=4:\sqrt 7$

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