Question

Two charges \(+5\,\mu C\) and \(-5\,\mu C\) form an electric dipole of length \(0.2\,m\). The dipole is placed in a uniform electric field of intensity \(20\,V\,m^{-1}\). If the angle between the dipole moment and electric field is \(30^\circ\), find the torque acting on the dipole.

• A. \(1\times10^{-5}\,N\,m\)
• B. \(2\times10^{-5}\,N\,m\)
• C. \(5\times10^{-6}\,N\,m\)
• D. \(1\times10^{-6}\,N\,m\)

Hint:

For an electric dipole in a uniform electric field, \[ \tau=pE\sin\theta. \] Maximum torque occurs when \(\theta=90^\circ\).

Answer 1

The Correct Option is C

Concept: An electric dipole placed in a uniform electric field experiences a torque given by \[ \tau = pE\sin\theta \] where \[ p=q\ell \] is the dipole moment.

Step 1: Calculate the dipole moment. Given, \[ q=5\times10^{-6}\,C \] and \[ \ell=0.2\,m \] Therefore, \[ p=q\ell \] \[ p=(5\times10^{-6})(0.2) \] \[ p=1\times10^{-6}\,C\,m \]

Step 2: Apply the torque formula. Given, \[ E=20\,V\,m^{-1} \] and \[ \theta=30^\circ \] Thus, \[ \tau=pE\sin\theta \] \[ =(1\times10^{-6})(20)\left(\frac12\right) \] \[ =10\times10^{-6} \] \[ =1\times10^{-5}\,N\,m \]

Step 3: Compare with the given options. The calculated value is \[ 1\times10^{-5}\,N\,m \] Therefore, mathematically the correct answer is \[ \boxed{(A)} \] The option key appears to contain an error.