An electric dipole of length 4 cm, when placed with its axis making an angle of $30^\circ$ with a uniform electric field, experiences a torque of $4\ \text{N m}$. Calculate the (i) magnitude of the electric field, (ii) potential energy of the dipole, if the dipole has charges of $\pm 10\,\text{nC}$.

(i) $E = 2 \times 10^{10}\ \text{N C}^{-1}$; (ii) $U = -4\sqrt{3}\ \text{J}$.

CBSE Class 12 · 2004 · ElectrostaticsShort Answer

An electric dipole of length 4 cm, when placed with its axis making an angle of

3 0^{\circ}

with a uniform electric field, experiences a torque of

4 N m

. Calculate the
(i) magnitude of the electric field,
(ii) potential energy of the dipole, if the dipole has charges of

\pm 10 nC

Answer: (i) $E = 2 \times 1 0^{10} N C^{- 1}$ ;
(ii) $U = - 43 J$ .

Solution

Dipole moment:

p = 10 \times 1 0^{- 9} \times 4 \times 1 0^{- 2} = 4 \times 1 0^{- 10} C m

(i) From

τ = pE sin θ

E = \frac{τ}{p sin 3 0 ^{\circ}} = \frac{4}{4 \times 1 0 ^{- 10} \times ( 1/2 )}

E = 2 \times 1 0^{10} N C^{- 1}

(ii) Potential energy:

U = - pE cos 3 0^{\circ} = - 4 \times 1 0^{- 10} \times 2 \times 1 0^{10} \times (3 /2)

U = - 43 J

CBSE Class 12 Board · 2004 · Subjective

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