Question

Two point charges of $3.2\times {10}^{-19}\text{C}$ and $-3.2\times {10}^{-19}\text{C}$ are seperated from each other by $2.4\times {10}^{-10}\text{m}$. The dipole is situated in a uniform electric field of intensity $4\times {10}^5\text{V/m}$. The work done in rotating the dipole by ${180}^{\circ }$ is $p\times {10}^{-24}\text{J}$. Find the value of $p$.

• A. 61.44
• B. 61
• C. 61.4

Answer 1

Answer: (A), (B), (C)

Given,

$q_1=3.2\times {10}^{-19}\text{C},q_2=-3.2\times {10}^{-19}\text{C}$

Seperation between two charges $d=2.4\times {10}^{-10}\text{m}$

From the data given in the question,

Dipole is placed in a uniform electric field of intensity $E=4\times {10}^5\text{V/m}$

Workdone in rotating the dipole by angle $\theta$ is given by

$W=pE(1-\cos \theta )$

But , given $\theta ={180}^{\circ }$.

$\therefore W=pE[1-(-1\left)\right]=2pE$

$\Rightarrow W=2\left(qd\right)E$

Substituting the given values we get,

$W=2\times 3.2\times {10}^{-19}\times 2.4\times {10}^{-10}\times 4\times {10}^5\text{J}$

$\Rightarrow W=61.44\times {10}^{-24}\text{J}$

Comparing this with , $x\times {10}^{-24}\text{J}$ we get, $x=61.44$

Accepted answers: $61,61.4,61.44$