An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field experiences a torque of $4 \sqrt{3} Nm .$ Calculate the
(i) magnitude of the electric field.
(ii) potential energy of the dipole, if the dipole has charges of ± 8nC.

Solution

Given,
length of the elctric dipole = 4cm= $4 \times 10^{- 2} m$

angle made with the elctric field- $θ = 60^{\circ}$

Torque experienced by the dipole- $τ$ = $4 \sqrt{3} N m$

charge on the dipole-q= $\pm 8 nC = \pm 8 \times 10^{- 9} C$

i) magnitude of Electric field-E

   $τ = pE sinθ = q \times 2 a \times E sinθ$

$\Rightarrow$    $4 \sqrt{3} = 8 \times 10^{- 9} \times 4 \times 10^{- 2} \times E \times \sin 60 °$
$\Rightarrow$ $E = \frac{4 \sqrt{3} \times 2}{32 \times 10^{- 11} \times \sqrt{3}} = \frac{1}{4} \times 10^{11} = 2.5 \times 10^{10} {NC}^{- 1}$

(ii) magnitude of potential energy of the dipole
   $U = - pE \cos θ$

$= - q \times 2 a \times E \cos θ$

   $= - 8 \times 10^{- 9} \times 2 \times 10^{- 2} \times 2.5 \times 10^{10} \cos 60 ° = - 2 J .$

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An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field experiences a torque of $4 \sqrt{3} Nm .$ Calculate the
(i) magnitude of the electric field.
(ii) potential energy of the dipole, if the dipole has charges of ± 8nC.

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An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field experiences a torque of $4 \sqrt{3} Nm .$ Calculate the
(i) magnitude of the electric field.
(ii) potential energy of the dipole, if the dipole has charges of ± 8nC.