Saved Bookmarks
| 1. |
Derive equation of potential energy of an electric dipole in a uniform electric field . |
Answer» Solution :Consider a dipole with charges -q and +q placed in a uniform electric field `vecE` as SHOWN in figure.  Dipole placed in a uniform electric field `vecE` at an angle `theta` Equal and opposite forces `+qvecE` and `-qvecE` are acting on charges -q and +q . The forces acting on dipole constitute moment of force and hence dipole experiences a torque `tau= vecpxx vecE` where `vecp=(2veca)q` which will tend to rotate it ( unless `vecp` is parallel or antiparallel to `vecE`). Suppose an external torque acting on dipole and it ROTATES with small angle `Deltatheta = theta_(1) - theta_(0)` the small work done, , `DeltaW= tau Deltatheta = p E sin theta d theta` Total work done during ROTATION from `theta_(0)` to `theta_(1)` `W= int_(theta0)^(theta) p E sin thetad theta` `= p E[ -cos theta]_(theta0)^(theta1)` `:. W = p E [ cos theta_(0)- cos theta_(1)]` This work is stored as the potential energy of the SYSTEM . `:.` Potential energy of dipole, `U = pE[ cos theta_(0)- cos theta_(1)]` Initially a dipole placed at an angle `theta_(0)=(pi)/(2)` and if it makes angle 6, = 0 from that position by ROTATING then the potential energy of dipole is `U=pE[cos""(pi)/(2)-costheta]` `=pE[0-cos theta]` `:. U=-pEcostheta` `:. U = -(vecp.vecE)` |
|