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An electric dipole is situated in an electric field as shown in figure. The dipole and electric field are both in the plane of paper. The dipole is rotated about an axis, perpendicular to the paper at point \(A\) in anti-clockwise direction. If the angle of rotation is measured with respect to the direction of the electric field, then the torque for different values of the angle of rotation \(\theta\) is correctly represented by which graph among \(a, b, c, d\) given in Fig \((b)\) ?
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Verified Answer
The correct answer is:
(b)
Torque on electric dipole placed in uniform electric field \(E\) is given as
\(\tau=p E \sin \theta\) ...(i)
where, \(p=\) electric dipole moment
and \(\theta=\) angle measured with respect to direction of electric field.
From Eq. (i),
When \(\theta=0^{\circ} \Rightarrow \tau=p E \sin 0^{\circ}=0\)
When \(\theta=\frac{\pi}{2} \Rightarrow \tau=p E \sin \frac{\pi}{2}=p E\)
When \(\theta=\pi \Rightarrow \tau=p E \sin \pi=0\)
When \(\theta=\frac{3 \pi}{2} \Rightarrow \tau=p E \sin \frac{3 \pi}{2}=-p E\)
When \(\theta=2 \pi \Rightarrow \tau=p E \sin 2 \pi=0\)
Hence, graph between \(\tau\) and \(\theta\) is given as
\(\tau=p E \sin \theta\) ...(i)
where, \(p=\) electric dipole moment
and \(\theta=\) angle measured with respect to direction of electric field.
From Eq. (i),
When \(\theta=0^{\circ} \Rightarrow \tau=p E \sin 0^{\circ}=0\)
When \(\theta=\frac{\pi}{2} \Rightarrow \tau=p E \sin \frac{\pi}{2}=p E\)
When \(\theta=\pi \Rightarrow \tau=p E \sin \pi=0\)
When \(\theta=\frac{3 \pi}{2} \Rightarrow \tau=p E \sin \frac{3 \pi}{2}=-p E\)
When \(\theta=2 \pi \Rightarrow \tau=p E \sin 2 \pi=0\)
Hence, graph between \(\tau\) and \(\theta\) is given as
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