Question

An electric dipole of length \(0.5 μ\text{m}\) is placed with its axis making an angle of \(30^{\circ}\) with uniform electric field \(10^4 \text{V/m}\). If it experiences a torque of \(5\times 10^{-9} \text{Nm}\), the magnitude of the charge on the dipole is (\(sin30^{\circ} = 0.5\))

• A. \(1 μ\text{C}\)
• B. \(1.5 μ\text{C}\)
• C. \(2 μ\text{C}\)
• D. \(2.5 μ\text{C}\)

Hint:

Torque is p E sin theta, with dipole moment p equal to q times length.

Answer 1

The Correct Option is C

Step 1: Plug in units
$L = 0.5\ \mu\text{m} = 5\times10^{-7}\ \text{m}$; $LE\sin\theta = 5\times10^{-7}\times10^4\times0.5 = 2.5\times10^{-3}$.

Step 2: Divide
$q = \frac{5\times10^{-9}}{2.5\times10^{-3}} = 2\times10^{-6}$ C. Option (C).

Final Answer:
2 microcoulomb. \[ \boxed{\text{(C)}\ 2\ \mu\text{C}} \]