An electric dipole with dipole moment \(4 × 10^{–9}\) C.m is aligned at 30° with the direction of a uniform electric field of magnitude \(5 × 10^4 NC^{–1}\) . Calculate the magnitude of the torque acting on the dipole.

Question Id: PH0000010

Question: An electric dipole with dipole moment \(4\times 10^{-9} C.m\) is aligned at 30° with the direction of a uniform electric field of magnitude \(5\times 10^{4} NC^{-1}\) . Calculate the magnitude of the torque acting on the dipole.

Answer: \( 10^{-4} Nm\) 

Explanation:

Given, 

Dipole moment (p)= \(4\times 10^{-9} C.m\)

Electric field (E)= \(5\times 10^{4} NC^{-1}\)

And \( \theta =30 \)

Fig-1: Torque acting on dipole due to electric field

We, know if angle between dipole moment \( p\) and electric field (E) is \( \theta\) then torque ( \( \tau \) ) acting on the dipole is 

\(\implies \tau =pE {sin \theta}\) 

\(\implies \tau = 4\times 10^{-9} \times 5\times 10^{4} \times {sin 30} \) 

\(\implies \tau = 4\times 10^{-9} \times 5\times 10^{4} \times \frac{1}{2} \) 

\(\implies \tau = 20 \times 10^{-5}  \times \frac{1}{2} \) 

\(\implies \tau = 10 \times 10^{-5} \) 

\(\implies \tau =  10^{-4} \)

Hence, torque ( \( \tau \) )  acting on the dipole is \( 10^{-4} Nm\) 

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N.B: If two equal and opposite point charge are kept at very short distance then the system is called electric dipole(p) . Direction of dipole is from negative charge to positive charge. 

But direction of electric field (E) for positive charge is away from the charge and for negative charge is towards the charge. 

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⭐ Related question answer from Reading tab:

1. What is the force between two small charged spheres having charges of \(2\times 10^{-7}C\) and \(3\times 10^{-7}C\) placed 30 cm apart in air?
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3. Four point charges qA = 2 µC, qB = –5 µC, qC = 2 µC, and qD = –5 µC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?
4. Explain the meaning of the statement ‘electric charge of a body is quantised'

5. Explain why two electrostatic field lines never cross each other at any point?

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