Question

An electric dipole consists of two charges +3 micro coulomb and -3 micro coulomb when held at 30° with respect to a uniform electric field of 10^4N/c experiences a torque of 9×10^-26Nm.calculate the length of the dipole.

Answer 1

Solution :

⏭ Given:

✏ Charge on dipole = 3$\mu$C

✏ Angle between dipole and electric field = 30°

✏ Magnitude of electric field = $10^4$N/C

✏ Torque experienced by dipole = 9 × $10^{-26}$Nm

⏭ To Find:

✏ Length of the dipole

⏭ Formula:

✏ Formula of torque experienced by dipole is given by...

$\star \: \underline{ \boxed{ \bold {\large{ \sf{ \pink{ \tau = PE\sin \theta}}}}}} \: \star$

✏ Formula of dipole moment is given by...

$\star \: \underline{ \boxed{ \bold{ \sf{ \large{ \blue{P = 2aq}}}}}} \: \star$

⏭ Terms indication:

✏ $\tau$ denotes torque

✏ P denotes dipole moment

✏ E denotes electric field

✏ $\theta$ denotes angle

✏ 2a denotes length of dipole

✏ q denotes charge on dipole

⏭ Calculation:

• Calculation of Dipole moment

$\implies \sf \: \red{ P = \dfrac{ \tau}{E \sin \theta} } \\ \\ \implies \sf \: P = \dfrac{9 \times {10}^{ - 26} }{ {10}^{4} \times \sin30 \degree } \\ \\ \implies \sf \: \underline{ \green{P = 18 \times {10}^{ - 30} \: Cm}}$

• Calculation of length of dipole

$\implies \sf \: \blue{2a = \dfrac{P}{q}} \\ \\ \implies \sf \: 2a = \dfrac{18 \times {10}^{ - 30} }{3 \times {10}^{ - 6} } \\ \\ \implies \: \underline{ \boxed{ \bold{ \sf{ \orange{ \large{Length \: of \: dipole = 6 \times {10}^{ - 24} \: m }}}}}}$

⏭ Additional information:

• In a uniform electric field, an electric dipole experiences no net forces but experiences a non-zero torque.
• As the net force on a dipole in a uniform electric field is zero, therefore, no linear acceleration is produced.
• Torque on a dipole becomes zero when it aligns itself parallel to the field.
• Torque on a dipole is maximum when it is held perpendicular to the field.