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.

Answer

a. `(-p q)/(2 pi epsilon_0 x^3)`
b. `( p q)/(2 pi epsilon_0 x^3)`
c. `(q p)/(4 pi epsilon_0 x^3)`.

Explanation

a. `E = (1)/(4 pi epsilon_0) q/(x^2)` (Fig. S3. 30).
`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.