Question

Consider a positively charged infinite cylinder with uniform volume charge density \(\rho>0\). An electric dipole consisting of +Q and -Q charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,

• A. a force to the left and no torque
• B. a force to the right and a clockwise torque
• C. a force to the right and a counter-clockwise torque
• D. no force but only a clockwise torque.

Answer 1

The Correct Option is B

Given: 

• An infinite cylinder with positive uniform charge density $\rho > 0$
• An electric dipole made of charges $+Q$ and $-Q$, connected by a massless rod
• The dipole is placed such that the two charges are at different distances from the axis

Electric field inside the cylinder:

The electric field at a distance $r$ from the axis is given by:
$\vec{E}(r) = \dfrac{\rho r}{2\varepsilon_0} \hat{r}$

This means the field is radially outward and increases with $r$.

Effect on the dipole:

• The $+Q$ charge is farther from the axis, so it experiences a stronger force outward.
• The $-Q$ charge is closer, so it experiences a weaker inward force.
• Thus, there is a net force to the right (outward).
• The forces form a couple (since they are not collinear), causing a clockwise torque.

Conclusion:

The dipole experiences a force to the right and a clockwise torque.

Correct option: (B): a force to the right and a clockwise torque

Answer 2

Consider a positively charged infinite cylinder with a uniform volume charge density ρ > 0.
An electric dipole consisting of +Q and -Q charges attached to opposite ends of a massless rod is oriented as shown in the figure
At the instant shown in the figure, the dipole will experience:
A force due to the electric field created by the charged cylinder.A torque that will try to align the dipole with the electric field.