Molecules B isolated atoms B have nonpolar molecules the centers of the positive and negative charges coincide (Fig. 24-11a) B showing the positively charged nucleus (green) and the negatively charged electrons (gold shading)

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24 Electric Potential Induced Dipole Moment

Many molecules, B water Bhave permanent electric dipole moments.

Molecules B isolated atoms B have nonpolar molecules the centers of the positive and negative charges coincide

(Fig. 24-11a) B showing the positively charged nucleus (green) and the negatively charged electrons (gold shading). B no dipole moment is set up.

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24 Electric Potential

(Fig. 24-11b) B a nonpolar molecule B put in an external electric field B the field distorts the electron orbits B and separates the centers of positive and negative charge

The electrons B tend to be shifted in a direction opposite the field B the shift sets up a dipole moment p B induced by the field B the atom or molecule B polarized by the field B when the field is removedB the induced dipole moment and the polarization

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24-10 Calculating the Field from the Potential

From Eq. 24-16 and Fig. 24-14 B the work done by the electric field may also be writ

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24 Electric Potential

s axis B X Û Y Û Z

S Bperpendicular to the B equipotential surfaces.

The component of the electric field B is zero in any direction parallel to the equipotential surfaces.

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24-11 Electric Potential Energy of a System of Point Charges Finding the electric potential energy of a system of charges due to the electric field produced by those same

charges.

Figure 24-15 shows B two point charges B q₁ Û q₂ separated by a distance B r.

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24 Electric Potential

Build the system B both charges infinitely far away and at rest.

Bring q₁ in B from infinity and put it in place,

No work do on B it B no electrostatic force acts on it.

Bring q₂₁ in B from infinity and put it in place,

There is work Bq_l exerts an electrostatic force on q₂ Using Eq. 24-8 B dropping the minus sign

The work B equal to B q₂V BV B set up by q_lat the point B where q₂ put

From Eq. 24-26 B the potential Ð

The electric potential energy B of the pair of point charges of Fig. 24-15 Ð

If the charges have the same sign B positive work B push them together against their mutual repulsion B the

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potential energy B positive

If the charges have opposite signs B negative work B against their mutual attraction B bring them together if they are B stationary B the potential energy B negative.