Question

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field of 10 dyne/C making 30º angle with \(\overrightarrow E\), the magnitude of torque acting on dipole is:

• A. \(1.0 × 10^{-8} Nm\)
• B. \(2.0 × 10^{-10} Nm\)
• C. \(4.0 × 10^{-10} Nm\)
• D. \(1.5 × 10^{-9} Nm\)

Hint:

To calculate the torque on a dipole, always ensure the units of electric field, charge, and distance are consistent. Convert non-SI units like dyne/C to N/C before substituting into the formula.

Answer 1

The Correct Option is B

The torque acting on an electric dipole in a uniform electric field is given by:

\[ \tau = pE \sin \theta, \]

where:

• \( p = q \cdot d \) is the dipole moment,
• \( E \) is the electric field intensity,
• \( \theta \) is the angle between \( \vec{p} \) and \( \vec{E} \).

Step 1: Calculate the dipole moment (\( p \)).
The dipole moment is: \[ p = q \cdot d = (0.01) \cdot (0.4 \times 10^{-3}) = 4 \times 10^{-6} \, \text{Cm}. \]

Step 2: Substitute values into the torque formula.
The electric field is given in dyne/C. Convert it to SI units: \[ 1 \, \text{dyne/C} = 10^{-5} \, \text{N/C}, \quad E = 10 \times 10^{-5} = 10^{-4} \, \text{N/C}. \] Now substitute the values: \[ \tau = (4 \times 10^{-6}) \cdot (10^{-4}) \cdot \sin 30^\circ. \]

Step 3: Simplify the expression.
\[ \sin 30^\circ = 0.5, \] so: \[ \tau = (4 \times 10^{-6}) \cdot (10^{-4}) \cdot 0.5 = 2 \times 10^{-10} \, \text{Nm}. \]