Question

Two point charges of $3.2\times {10}^{-19}C$ and $-3.2\times {10}^{-19}C$ are separated from each other by $2.4\times {10}^{-10}m$.The dipole is situated in a uniform electric field of intensity $4\times {10}^{5}V{m}^{-1}.$ If the work done in rotating the dipole by ${180}^{\circ }$ is $n\times {10}^{-23}J$, the value of $n$ is . (Write upto two decimal places)

Answer 1

Initially the dipole must be aligned in the direction of electric field so that the dipole is in equilibrium .
It means that the angle between the dipole vector and electric field vector is $0^{\circ }$.
${\theta }_1=0^{\circ }$
As the dipole is rotated by ${180}^{\circ }$, so ${\theta }_2={180}^{\circ }$

We know that, work done in rotating the dipole by ${180}^{\circ }$ is
$W=\Delta U=U_f-U_i=-PEcos{\theta }_2-(-PEcos{\theta }_1)$
$⟹W=PEcos\left(0^{\circ }\right)-PEcos\left({180}^{\circ }\right)$
$⟹W=2PE$
$⟹W=2\times 2.4\times {10}^{-10}\times 3.2\times {10}^{-19}\times 4\times {10}^5$
$\therefore W=6.1\times {10}^{-23}J$