A dipole consisting of charges plus and minus e, 220 nm apart, is placed between

Question

A dipole consisting of charges plus and minus e, 220 nm apart, is placed between two very large (essentially infinite) sheets carrying equal but opposite charge densities of 125 C/m2 . (a) What is the maximum potential energy this dipole can have due to the sheets, and how should it be oriented relative to the sheets to attain this value? (b) What is the maximum torque the sheets can exert on the dipole, and how should it be oriented relative to the sheets to attain this value? (c) What net force do the two sheets exert on the dipole?

Explanation / Answer

We potential energy of the dipole is U = -p.E = -pE cos p = dipole moment = q*l =(1.6*10-19C)* 220*10-9m =3.52*10-26Cm l = distance between the charges = 220 nm =220*10-9m q = charge magnitude =e = 1.6*10-19C For U to be maximum then angle of orientation =180 deg Then U max=  -pE cos180 = pE =(3.52*10-26Cm )*(14.117*106N/C)                                                  = 49.69*10-20J E = electric field between the two sheets =/0 =(125*10-6C/m2)/ 8.854*10-12C2/Nm2                                                              = 14.117*106N/C                                                              = 14.117*106N/C 0 =8.854*10-12C2/Nm2 = charge density of sheet =125C/m2 = 125*10-6C/m2 b) torque acting on the dipole is = p X E =pEsin Then torque to be maximum then sin = 1 Then maximum torque max = pE = 3.52*10-26Cm )*(14.117*106N/C)                                                  = 49.69*10-20Nm                                                  = 49.69*10-20Nm c) net force acting on the dipole is zero. Because the force + e and -e are opposite in direction andequal in magnitude.

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