Ncert Exercises & Solutions

1.27 In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of $10^{5} {NC}^{- 1}$ per meter. What are the force and torques experienced by a system having a total dipole moment equal to $10^{- 7}$ Cm in the negative z-direction?

The dipole moment of the system, $p = q x dl = - 10^{- 7} Cm$

Rate of increase of electric field per unit length,

$\frac{d E}{d l} = 10^{5} N C^{- 1}$

Force (F) experienced by the system is given by the relation,

$\begin{array}{l} F = q E = q \times \frac{d E}{d l} \times d l = q \times d l \times \frac{d E}{d l} = p \times \frac{d E}{d l} \\ = - 10^{- 7} \times 10^{5} \\ = - 10^{- 2} N \end{array}$

The force is $- 10^{- 2}$ N in the negative z-direction i.e., opposite to the direction of the electric field. Hence, the angle between the electric field and the dipole moment is 180°. Torque ( $ζ$ ) is given by the relation,T =pE sin 180° = 0

Therefore, the torque experienced by the system is zero.

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