Dipole in Field of Point Charge
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Exercise:
A dipole is placed in the field of a po charge with its dipole moment vec p q vec d ed in the direction of the field lines. abcliste abc Show that for a distance r from the po charge Q with r gg d the force acting on the dipole can be written as F - k_C fracQ pr^ abc Calculate the force on an HCl hydrochloric acid molecule at a distance rO from a H^+ ion. The dipole moment of an HCl molecule is pO. Compare the result to the force acting on an electron at the same distance. abcliste
Solution:
abcliste abc The forces on the positive and negative charge of a dipole at distance r from a po charge Q are F_+ q E_Qr+d/ q k_C fracQr+d/^ F_- -q E_Qr-d/ -q k_C fracQr-d/^ where we ase a simple dipole with its negative charge facing the po charge see figure. The net force is thus F q k_C Q leftfracr+d/^ - fracr-d/^ right k_C q Q fracr-d/^ - r+d/^r+d/^ r-d/^ k_C q Q fracr^+d^/-rd - r^+d^/+rdr^-d^/^ &approx k_C q Q frac-rdr^ - k_C Q q d fracr^ - k_C fracQ pr^ In this situation the force pos towards the po charge negative sign. abc The force acting on the molecule is F FF timeskCtimesfracncetimespr^ resultFS The force on an electron at the same distance would be F' FeF kC times fracnce^r^ resultFeS The force on the dipole is much weaker than that on the electron. abcliste
A dipole is placed in the field of a po charge with its dipole moment vec p q vec d ed in the direction of the field lines. abcliste abc Show that for a distance r from the po charge Q with r gg d the force acting on the dipole can be written as F - k_C fracQ pr^ abc Calculate the force on an HCl hydrochloric acid molecule at a distance rO from a H^+ ion. The dipole moment of an HCl molecule is pO. Compare the result to the force acting on an electron at the same distance. abcliste
Solution:
abcliste abc The forces on the positive and negative charge of a dipole at distance r from a po charge Q are F_+ q E_Qr+d/ q k_C fracQr+d/^ F_- -q E_Qr-d/ -q k_C fracQr-d/^ where we ase a simple dipole with its negative charge facing the po charge see figure. The net force is thus F q k_C Q leftfracr+d/^ - fracr-d/^ right k_C q Q fracr-d/^ - r+d/^r+d/^ r-d/^ k_C q Q fracr^+d^/-rd - r^+d^/+rdr^-d^/^ &approx k_C q Q frac-rdr^ - k_C Q q d fracr^ - k_C fracQ pr^ In this situation the force pos towards the po charge negative sign. abc The force acting on the molecule is F FF timeskCtimesfracncetimespr^ resultFS The force on an electron at the same distance would be F' FeF kC times fracnce^r^ resultFeS The force on the dipole is much weaker than that on the electron. abcliste