Question 781: Electrostats & Capacitance

Question

An electric dipole having each charge of magnitude $2 \mu \mathrm{C}$ is placed in an electric field of intensity $8 	imes 10^{+4} \mathrm{~N} / \mathrm{C}$. If the maximum torque acting on the dipole is $4 	imes 10^{-3} \mathrm{~N}-\mathrm{m}$, the length of the dipole is

Accepted Answer

Given:
Charge on each dipole end, $q = 2\,\mu	ext{C} = 2 	imes 10^{-6}\,	ext{C}$
Electric field, $E = 8 	imes 10^4\, 	ext{N/C}$
Maximum torque, $	au_{max} = 4 	imes 10^{-3}\,	ext{N-m}$
The formula for maximum torque on a dipole in a uniform electric field is:
$$ 	au_{max} = pE $$
where $p$ is the dipole moment.
Dipole moment, $p = q 	imes 2a$ (where $2a$ is the length of dipole).
So,
$$ 	au_{max} = (q 	imes 2a) E $$
Solving for $2a$ (dipole length):
$ 2a = \frac{	au_{max}}{qE} $
Substitute the values:
$ 2a = \frac{4 	imes 10^{-3}}{2 	imes 10^{-6} 	imes 8 	imes 10^4} $
Calculate the denominator:
$ 2 	imes 10^{-6} 	imes 8 	imes 10^4 = 16 	imes 10^{-2} = 0.16 $
Now,
$ 2a = \frac{4 	imes 10^{-3}}{0.16} $
$ 2a = \frac{4}{0.16} 	imes 10^{-3} $
$ 2a = 25 	imes 10^{-3} 	ext{ m} $
Converting meters to millimeters ($1 	ext{ m} = 1000 	ext{ mm}$):
$ 2a = 25 	imes 10^{-3} 	imes 1000 = 25	ext{ mm} $
Correct answer:
Option B: 25 mm

Answer

10 mm

Answer

25 mm

Answer

15 mm

Answer

20 mm

Electrostats & Capacitance

An electric dipole having each charge of magnitude 2 \mu \mathrm{C} is placed in an electric field of intensity 8 \times 10^{+4} \mathrm{~N} / \mathrm{C}. If the maximum torque acting on the dipole is 4 \times 10^{-3} \mathrm{~N}-\mathrm{m}, the length of the dipole is

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