Problem 6. E=(Cx}3? XH AXr-f ii An electric dipole consists of charge q at position .1: and a second charge +q at position :1: + A2: on the ar-axis as shown. This dipole is in a nonuniform electric eld E = (02:) 56-, where C is a (given) constant. a) What is the (vector) dipole moment of this electric dipole 15' in terms of the givens. b) Sum the total electrostatic force acting on the two charges that make up the dipole, and write the result in terms of pm, the m-component of the dipole mo- ment. 0) Show that in the limit that Ax > 0 your answer to b) can be written: evaluated "at" 2:. Fa: _ dEx i d1: dU \"Ea Part c explanation We have, E = Ex = ((x ) 2 Since there is no y-comp. even the net force has no y comp. 1.e . F = fu . As Ex only depends on x, SEX, change in electric field wir. t. change in X ? AX lim Ex . dEx - d ( (x] m = Cx ( From differentiation) dugets its 931 (1 ) . From ( b), F = Fx = (CPx) " = Px CR - --(2). Replacing value for (1) in (2), 1 working F 2 Fuz PadEx = den pen - -. ( shown ) We know, work done du ( small work ) against F during small disp. ( d x) 2 (02 angle beth F & doe du . F d x (-1 ) = 180" = since were done - du ( 3 ) - potential energy - 2 F 2 work done against the force From ( 2) 2 ( 3) FX = dEx py = = du