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-Atomic View of Dielectrics -Electric Dipole in an Electric Field -Partially Filled Capacitors AP Physics C Mrs. Coyle Atomic View of Dielectrics: The molecules of the dielectric are modeled as dipoles External E-Field No External E-Field Random orientation of molecules Partial Alignment of Molecules Force Acting by a Uniform External Field on the Dipole Note: E is not the field produced by the dipole The force acting on each charge is F = Eq The net force on the dipole is zero The forces produce a net torque on the dipole p=2aq 2a = 2Fa sin = pE sin =pxE Electric Dipole Moment, p The electric dipole moment (p) is a vector directed along the line joining the charges from – q to +q , A dipole has two equal but opposite sign charges Assume the distance between the charges is 2a p=2aq Work Required to Rotate the Dipole will result in an Increase in the Potential Energy of the Dipole-External Field System dW d f W U f U i d i U f -U i = pE(cos i - cos f ) Assume i 90o , U i 0 = pE sin Uf -Ui = - pE cos U= - p · E An external field can polarize the dielectric whether the molecules are polar or nonpolar The charged edges of the dielectric act as a second pair of plates producing an induced electric field in the direction opposite the original electric field The degree of alignment of the molecules with the field depends on temperature and the magnitude of the field. Generally: the alignment increases with increasing field strength the alignment increases with decreasing temperature Non Polar Dielectrics The electric field produces some charge separation This produces an induced dipole moment The effect is then the same as if the molecules were polar Induced Charge and Field The electric field due to the plates is directed to the right and it polarizes the dielectric The net effect on the dielectric is an induced surface charge that results in an induced electric field If the dielectric were replaced with a conductor, the net field between the plates would be zero Geometry of Some Capacitors Example – Partially Filled Capacitor o A Co , Capacitance without dielectric d +Q d 3 d -Q A What is the capacitance in terms of Co? Hint: Two capacitors in series. Ans: 3 C C0 2 1