Question

Two opposite and equal charges of magnitude $4\times {10}^{-8}$ coulomb when placed $2\times {10}^{-2}$ cm apart from a dipole. if this dipole is placed in an external electric field of $4\times {10}^{8}N/C$ , the value of maximum torque and the work done in rotaing it through 180 degree will be:

• A. $6.4\times {10}^{-3}J$
• B. $32\times {10}^{-4}J$
• C. $32\times {10}^{-3}J$
• D. $64\times {10}^{-4}J$

Answer 1

The correct option is D $64\times {10}^{-4}J$

$Given:$ $q=4\times {10}^{-8}C$

$2a=2\times {10}^{-2}cm$

$E=4\times {10}^{8}N/C$

$Solution:$ Now, dipole moment= $q\times 2a$

For maximum Torque $=\overrightarrow{p}\times \overrightarrow{E}$

$=q\times 2a\times E$

$=4\times {10}^{-8}\times 2\times {10}^{-2}\times 4\times {10}^8$

$=32\times {10}^{-2}Ncm$

$=32\times {10}^{-4}Nm$

$\therefore$ $$\begin{array}{cc}\text{work done}& =2pE\left(For{180}^o\right)\\ & =2\times 32\times {10}^{-4}=64\times {10}^{-4}J\end{array}$$

$So,the$ $correct$ $option:D$