Summary we have seen that in quantum optics the em field is represented as a set of independent quantized harmonic oscillators of energy 1 hoa(t)a (t) (1.53) moreover, we express the vector potential and the electric field in terms of plane determined by the creation à and annihilation à operators waves whose amplitudes are quantized and eral description and quantization of em fields associated with the mode k of the field as - hc] (1.54) hop k 4(+) = e (f, t)+(f, t), (1.55) where h. c. stands for the hermitian conjugate of the first term in the bracket, and (- e 4(+) f, t) hox -en(t) ek. (1.56) 260v (f. i-(0', the constant ha/(2e0v) is called the quantum unit of electric strength

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Dinate system, and a charge q = - 2.00 nc is placed s2 10 n> c. (a) what is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to es from parallel to perpendicular? (b) at what absolute temperature t is the average translational kinetic energy 32 kt of a molecule equal to the change in potential energy calculated in part(: abovethistemperature,thermalagitationprevents the dipoles from aligning with the electric field.) placed in a uniform electric field e with magnitude 1.6 * 6 on the positive x-axis at x = 4.00 cm. (a) if a third charge q3 = +6.00 nc is now placed at the point x = 4.00 cm, y = 3.00 cm, find the x- and y-components of the total force exerted on this charge by the other two. (b) find the magnitude and direction of figure p21.62 ll uu 21.55 . torque on a dipole. an electric dipole with dipole moment ps is in a uniform external electric field es. (a) find the orientations of the dipole for which the torque on the dipole is zero. (b) which of the orientations in part (a) is stable, and which is unstable? (hint: consider a small rotation away from the equi- librium position and see what happens.) (c) show that for the stable orientation in part (b), the dipole’s own electric field tends to oppose the external field. 21.62 ..

A10 kg box initially at rest is pulled 18 meters across a horizontal, frictionless surface by a 40 n force. what is the block’s final velocity over the 18 meters?