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To express such distributed field-lines mathematically, we can utilize an induction effect on a conductor by an applied electric field, known as electrostatic induction or polarization. Due essentially to mobile charges, a material placed in a condenser can be polarized by an applied electric field, exhibiting positive and negative charges on surfaces close to the negative and positive capacitor plates, respectively. 5. 6, we indicate locations of displaced charges schematically by small filled and open circles for positive and negative charges, respectively.

Closing S2 , however, the charges on C1 are redistributed between the two capacitors C1 and C2 . 7(c), it is noted that the total charge Q 1 + Q 2 is constant, and the capacity of the two capacitors connected in parallel is effectively equivalent to a single capacity C given by C= Q1 + Q2 Q1 Q2 = + = C1 + C2 . 11) 26 2. 11) can be extended to parallel connections of more than two capacitors, for which we obtain the formula, C = Ci , where i = 1, 2, . . , Q 1 = Q 1 +Q 2 . On the other hand, it is noted that the stored energies before and after redistribution are not identical, as seen from the following calculation: The initial energy stored in C1 is given by U1 = 12 Q 21 /C1 , whereas after the redistribution, the final energy stored in both capacitors is U = 12 Q 12 /C1 + 12 Q 22 /C2 .

26a) as related to the torque ␶ = p×E where |␶ | = p E sin␪. 26b) Here ␪ is the angle between the vectors p and E. 26b). Such a force is responsible for translational motion of the dipole. , E(x + dx) − E(x) = (∂ E/∂ x) dx, where dx = lcos␪, and therefore the net force is given by F =q ∂E ∂E l cos ␪ = p cos ␪ . 3. The Dipole-Dipole Interaction In dielectric materials, polar molecules can be represented by their dipole moments. In this case, the mutual interaction energy arises from dipole-dipole interactions.

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