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 105 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,

dEdl=105NC1

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

F=qE=q×dEdl×dl=q×dl×dEdl=p×dEdl=107×105=102N

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.