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:
Show 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.
- \(1.0 × 10^{-8} Nm\)
- \(2.0 × 10^{-10} Nm\)
- \(4.0 × 10^{-10} Nm\)
- \(1.5 × 10^{-9} Nm\)
The Correct Option is B
Solution and Explanation
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:
\[
\tau = (4 \times 10^{-6}) \cdot (10^{-4}) \cdot 0.5 = 2 \times 10^{-10} \, \text{Nm}.
\]
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