Question 54: Electrostatics & Capacitance

Question

Two electric dipoles of dipole moments $3.9 	imes 10^{-30} \mathrm{Cm}$ and $5.2 	imes 10^{-30} \mathrm{Cm}$ are placed in two different uniform electric fields of strengths $16 	imes 10^4 \mathrm{NC}^{-1}$ and $4 	imes 10^4 \mathrm{NC}^{-1}$ respectively. What is the ratio of maximum torque experienced by the electric dipoles?

Accepted Answer

LetÃ¢ÂÂs use the fact that the maximum torque on a dipole is
$$	au_{\max}=p\,E.$$
So for the two dipoles:
Dipole 1:
Ã¢ÂÂ¢ $p_1=3.9	imes10^{-30}\,\mathrm{Cm}$
Ã¢ÂÂ¢ $E_1=16	imes10^4\,\mathrm{N/C}=1.6	imes10^5\,\mathrm{N/C}$
Ã¢ÂÂ¢ $	au_1=p_1E_1=(3.9	imes10^{-30})(1.6	imes10^5)=6.24	imes10^{-25}\,\mathrm{N\,m}$
Dipole 2:
Ã¢ÂÂ¢ $p_2=5.2	imes10^{-30}\,\mathrm{Cm}$
Ã¢ÂÂ¢ $E_2=4	imes10^4\,\mathrm{N/C}$
Ã¢ÂÂ¢ $	au_2=p_2E_2=(5.2	imes10^{-30})(4	imes10^4)=2.08	imes10^{-25}\,\mathrm{N\,m}$
Ratio
$$ \frac{	au_1}{	au_2}=\frac{6.24	imes10^{-25}}{2.08	imes10^{-25}}=3:1. $$
Answer: Option D (3 : 1).

Answer

$12: 1$

Answer

$9: 1$

Answer

$1:9$

Answer

$3: 1$

Electrostatics & Capacitance

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