An electric dipole consists of two opposite charges each of magnitude 1 mC separated by 2 cm. The dipole is placed in an external uniform field of `10^5 NC^-1` intensity. Find the
a. maximum torque exterted by the field on the dipole, and
b. work done in roating the dipole through `180^(@)` starting from the position `theta = 0^(@)`.

Explanation

Here, `E = 10^5 NC^-1 , q = 1 mu C = 10^(-6) C , 2 a = 2 cm = 0.02 m`
`p = q(2 a) = 10^-6 xx 0.02 = 2 xx 10^-8 cm`
a. The torque acting on a dipole is given by
`tau = p E sin theta`
Torque is maximum when `sin theta = 1`
`tau_(max) = 2 xx 10^-8 xx 10^5 xx 1 = 0.002 Nm`
b. Now, work done in rotating the dipole from `theta = theta_1` to `theta = theta_2` is given by
`W = p E (cos theta_1 - cos theta_2)`
Here, `theta_1 = 0^(@), theta_2 = 180^(@)`. Therefore,
`W = 2 xx 10^-8 xx 10^5 (cos 0^(@) - cos 180^(@))`
=`0.002 [1-(-1)] = 0.004 J`.