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Homework Statement
An electric dipole with magnitude ##p = 0.2Cm## is placed inside a uniform electric field of ##\vec{E} = 100\vec{i} + 70\vec{j} + 40\vec{k} \frac {N} {C}##. The dipole was initially pointing along the +x direction. You then start to rotate it first on xz-plane towards the z-axis. After it is aligned with the z-axis, you rotate it on the yz-plane towards the y-axis. At the final moment, the dipole is aligned parallel to the +y axis.
(a) What is the total work done by you during this process?
(b)In the final orientation, the electric field applies a torque ~ τ on the dipole. As you want to keep the dipole in this orientation, you apply another torque ~ τhand to prevent it from rotating. Find both torques.
Homework Equations
##\vec {τ}=\vec {p}x\vec {E}##
##W=τΔθ##
The Attempt at a Solution
Our dipole moment is ##\vec {p}=(0,2\vec{i})## and ##\vec{E} = 100\vec{i} + 70\vec{j} + 40\vec{k} \frac {N} {C}## is so
##\vec{τ}=\vec {p} x \vec {E}=(-8\vec{j}+14\vec{k})## and the magnitude is ##16.1Nm##
Its uniform electric field so I think we don't need an integral.Or the integral becomes
##W=τΔθ##
In the first rotation The electric field wlll going to rotate the dipole.But I think we need an extra torque to make it turn just 90 degree so I am little bit confused after here.I think I don't have enough info to calculate the torque done by me or work ?