Two opposite and equal charges 4 x 10^-8 Coulomb when placed 2 x 10 ^-2 cm apart form a dipole - Physics - Electric Charges And Fields

Question

Two opposite and equal charges 4 x 10^-8 Coulomb when placed 2 x 10
^-2 cm apart form a dipole is placed in an external electric field
4 x 10^8 N/C, the value of maximum torque and the work done in
rotating it through 180° from its initial orientation which is
along electric field will be

Ved Prakash Lakhera · Accepted Answer

The toque due a dipole placed in an electric field is given by:                τ^ = P^×E^=P E sinθBut P=ql=4×10-8×2×10-2×10-2=8×10-12Cm  and  E=4×108N/C Since the initially θ=0° so torque τ = 0Therefore maximum torque τmax= P E sin90° =P E =8×10-12×4×108=3
2×10-3Nm The workdone by this torque=W=∫0πτ dθ=∫0πP E sinθ dθ=P× E -cosθ0πor               W=P E -cosπ+-cos0°=P× E 1+1=2P× Eso         Workdone by torque τ = 2×3
2×10-3Nm =6 4×10-3J

Two opposite and equal charges 4 x 10^-8 Coulomb when placed 2 x 10 ^-2 cm apart form a dipole is placed in an external electric field 4 x 10^8 N/C, the value of maximum torque and the work done in rotating it through 180° from its initial orientation which is along electric field will be