Two charges of each 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 E → of 10 dyne · C - 1 making 30 ∘ an

Question

Two charges of each 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 E → of 10 dyne · C - 1 making 30 ∘ angle with E → , the magnitude of torque acting on dipole is:

TestHub · Accepted Answer

The formula to calculate the dipole moment is given by
$|\overset{⇀}{p}| = q |\overset{⇀}{d}| . . . (1)$
Substitute the values of the known parameters into equation (1) to calculate the dipole moment.
$\begin{array}{rcl} |\overset{⇀}{p}| & = & 0.01 C \times 0.4 mm \times \frac{1 m}{10^{3} mm} \\ = & 4.0 \times 10^{- 6} C \cdot m \end{array}$
The formula to calculate the torque on the dipole in the electric field is given by
$| \vec{τ} | = | \vec{p} \times \vec{E} | . . . (2)$
Substitute the values of the known parameters into equation (2) to calculate the required torque.
$\begin{array}{rcl} |\overset{⇀}{τ}| & = & 4.0 \times 10^{- 6} C \cdot m \times 10 dyne \cdot C^{- 1} \times \frac{1 N}{10^{5} dyne} \times \sin 30 ° \\ = & 2 \times 10^{- 10} N m \end{array}$

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