Question

An electric dipole with dipole moment \(5\times10^{-7}\ \text{C m}\) is in the electric field of
\[ 2\times10^4\ \text{N C}^{-1} \] at an angle of \(60^\circ\) with the direction of the electric field. The torque acting on the dipole is

• A. \(9\times10^{-3}\ \text{N m}\)
• B. \(1\times10^{-4}\ \text{N m}\)
• C. \(8.66\times10^{-3}\ \text{N m}\)
• D. \(2.88\times10^{-3}\ \text{N m}\)

Hint:

The torque on an electric dipole is maximum when the dipole is perpendicular to the electric field, i.e., when \(\theta=90^\circ\).

Answer 1

The Correct Option is C

Step 1: Recall the torque on a dipole.
A dipole of moment $p$ in a uniform field $E$, tilted by angle $\theta$ to the field, feels a turning effect \[ \tau = pE\sin\theta. \]
Step 2: List the given values.
$p = 5\times10^{-7}\ \text{C m}$, $E = 2\times10^{4}\ \text{N C}^{-1}$, and $\theta = 60^\circ$.
Step 3: Compute the product $pE$.
\[ pE = (5\times10^{-7})(2\times10^{4}) = 10\times10^{-3} = 10^{-2}\ \text{N m}. \]
Step 4: Bring in the angle factor.
Since $\sin 60^\circ = \dfrac{\sqrt3}{2} \approx 0.866$, \[ \tau = 10^{-2}\times 0.866. \]
Step 5: Evaluate.
\[ \tau = 8.66\times10^{-3}\ \text{N m}. \]
Step 6: Conclude.
The dipole experiences a torque of about $8.66\times10^{-3}\ \text{N m}$.
\[ \boxed{8.66\times10^{-3}\ \text{N m}} \]