Question

An electric dipole placed in a nonuniform electric field may experiences:

• A. a force but no torque
• B. a torque but no force
• C. a force as well as a torque
• D. neither a force nor a torque

Answer 1

Answer: (C)

a force as well as a torque

I ) Force
$\to$ If the electric field is nonuniform then force is non-zero,
At charge A $F_A=q\overrightarrow{E_1}$
and at B $F_B=(-q)\overrightarrow{E_2}$
$\therefore$ total net force on the system $=q(\overrightarrow{E_1}-\overrightarrow{E_2})$
( $E_1\pm E_2$ as nonuniform electric field )
II ) Torque
As given in above diagram $F_A=EQ\hat{i}$
$F_B=-EQ\hat{i}$
$\therefore$ Torque acting about middle point $C=EQdsin\theta$
$Torque=\overrightarrow{P}\times \overrightarrow{E}$