Question

Two equal and opposite charges of $4\times {10}^{-8}$ C when placed $2\times {10}^{-2}cm$ away, form a dipole. If this dipole is placed in an external electric field of $4\times {10}^8$ newton/coulomb, the value of maximum torque and the work done in rotating it through ${180}^{\circ }$ will be

• A. $64\times {10}^{-4}Nmand64\times {10}^{-4}J$
• B. $32\times {10}^{-4}Nmand32\times {10}^{-4}J$
• C. $64\times {10}^{-4}Nmand32\times {10}^{-4}J$
• D. $32\times {10}^{-4}Nmand64\times {10}^{-4}J$

Answer 1

The correct option is D $32\times {10}^{-4}Nmand64\times {10}^{-4}J$

Dipole moment $p=4\times {10}^{–8}\times 2\times {10}^{–4}=8\times {10}^{–12}Cm$
Maximum torque = $pE=8\times {10}^{–12}\times 4\times {10}^8$
$=32\times {10}^{–4}Nm$
Maximum work done in rotating through ${180}^{\circ }=2pE$
$=2\times 32\times {10}^{–4}=64\times {10}^{–4}J$