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: Use the formula for torque on an electric dipole.
Torque acting on an electric dipole placed in a uniform electric field is given by
\[ \tau=pE\sin\theta \]
where
\[ p=5\times10^{-7}\ \text{C m} \] is the dipole moment,
\[ E=2\times10^4\ \text{N C}^{-1} \] is the electric field strength, and
\[ \theta=60^\circ \] is the angle between dipole moment and electric field.

Step 2: Substitute the given values.
\[ \tau=(5\times10^{-7})(2\times10^4)\sin60^\circ \]
Since
\[ \sin60^\circ=\frac{\sqrt3}{2} \]
\[ \tau=(10\times10^{-3})\times\frac{\sqrt3}{2} \]
\[ \tau=10^{-2}\times0.866 \]
\[ \tau=8.66\times10^{-3}\ \text{N m} \]

Step 3: Final conclusion.
Hence, the torque acting on the dipole is
\[ \boxed{8.66\times10^{-3}\ \text{N m}} \]