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A short dipole is placed along the x - axis at x = x (Fig. 3.120). . a. Find the force acting on the dipole due to a point charge q placed at the origin. b. Find the force on the dipole if the dipole is rotated by 180^(@) about the z- axis. c. Find the force on dipole if the dipole is rotated by 90^(@) anticlockwise about z - axis, i.e., it becomes parallel to the y - axis. |
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Answer» `U = - p E cos 0^(@) = - (q p)/(4 pi epsilon_0 x^2)`  `F = - (del U)/(del x) = (- p q)/(2 pi epsilon_0 x^3)` NEGATIVE sign indicates that force on DIPOLE is toward the positive x - direction or the force is attractive. b. `U = - pE cos 180^(@) = (q p)/(4 pi epsilon_0 x^2)` `F = - (del U)/(del x) = (p q)/ (2 pi epsilon_0 x^3)` (##BMS_V03_C03_E01_062_S02##). Positive sign indicates that force on dipole is toward the positive x - direction or the force is REPULSIVE. c. `E = (1)/(4 pi epsilon_0) P/(x^3)` Let us first force on q due to P.  `F = q E = (q p)/(4 pi epsilon_0 x^3)` Charges q will also apply the same force on dipole but in an opposite direction, so the force on dipole is `F = (q p)/(4 p[i epsilon_0 x^3)` along `vec p` or parallel to y - axis. |
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