Lectures 7 & 8 Electric Potential – continuous charge distributions To calculate E produced by an electric dipole To investigate the forces and torques an electric dipole experiences in an external E-field Importance: Production and reception of radio and TV signals Interaction of molecules with EM radiation: - molecular spectroscopy - trace analysis Electric Dipoles

V of an Infinite Wire of Uniform Charge per Unit Length

V of a spherical volume of uniform charge, of radius a, carrying a total charge Q (i) (ii) Q R

l +q+q-q-q V due to the two charges at P Assumption: r >> l r-r- r+r+ P  r l/2 Electric Dipole: Calculation of the E-field at an arbitrary (r,  )

-q-q +q+q p l E qEqE -qE No Net Force But Torque  - rotates the dipole clockwise An Electric Dipole in an External E-Field

Torque (of a couple) The resultant torque is: Torque of a couple is the same about any axis drawn perpendicular to the plane it defines The magnitude of the torque of a couple is calculated from

-q-q +q+q l qE -qE  d The torque tends to align p and E

+q+q qEqE -qE -q The P.E. of an electric dipole in an E-field work done  change in P.E Work done by  during an infinitesimal displacement d  : The torque is in the direction of decreasing  Hence

Finite displacement from  1 to  2 : Therefore Work = -change of P.E. Thus the P.E. of an electric dipole in an E-field is: Minimum at  = 0, maximum at  = , and zero at  =  /2

Review and Summary An electric dipole is a pair of electric charges of equal magnitude q but opposite sign, separated by a distance l The electric dipole moment is defined to have magnitude p = ql We calculate the E of an electric dipole at any position in space by a method far easier than using Coulomb’s law and superposition