Question

The figure given below shows four orientations of an electric dipole in an external electric field.

• A. Potential energy of dipole is greater for orientations $\left(1\right)$ and $\left(3\right)$ than $\left(2\right)$ and $\left(4\right)$.
• B. If the dipole rotates from orientation $\left(1\right)$ to $\left(2\right)$, then the workdone on the dipole by field is positive.
• C. If the dipole rotates from orientation $\left(1\right)$ to $\left(2\right)$, then the workdone on the dipole by field is negative.
• D. Workdone to rotate dipole from $\left(1\right)$ to $\left(2\right)$ is same as workdone to rotate dipole from $\left(1\right)$ and $\left(4\right)$.

Answer 1

Answer: (A), (B), (D)

Workdone to rotate dipole from $\left(1\right)$ to $\left(2\right)$ is same as workdone to rotate dipole from $\left(1\right)$ and $\left(4\right)$.

From the given figure, we can deduce that, Angle made by the dipole with electric field in orientations $\left(1\right)$ and $\left(3\right)$ is same. Similarly, angles made by the dipole in orientations $\left(2\right)$ and $\left(4\right)$ with electric field are same.

$\therefore$ Potential energy of dipole in orientation $\left(1\right)$ is given by

$U_1=-pE\cos (180-\theta )=pE\cos \theta ....\left(a\right)$

Thus, we can say that , $U_3=pE\cos \theta ......\left(b\right)$

Similarly,

Potential energy of dipole in orientation $\left(2\right)$ is given by $U_2=-pE\cos \theta .......\left(c\right)$

Thus, $U_4=-pE\cos \theta ......\left(d\right)$

Hence, option (a) is correct.

Workdone on the dipole by field while rotating from $\left(1\right)$ to $\left(2\right)$ is

$W=U_i-U_f=U_1-U_2$

Substituting $\left(a\right)$ and $\left(c\right)$,

$\Rightarrow W=2pE\cos \theta .......\left(e\right)$

Since, workdone is positive, we can say that, option (b) is correct.

Workdone on the dipole by field while rotating from $\left(1\right)$ to $(4$ is

$W^{\prime }=U_i-U_f=U_1-U_4$

Substituting $\left(a\right)$ and $\left(d\right)$

$\Rightarrow W^{\prime }=2pE\cos \theta .......\left(f\right)$

From $\left(e\right)$ and $\left(f\right)$ we can conclude that, $W=W^{\prime }$

So, option (d) is also correct.

Hence, options (a) , (b) and (d) are the correct answers.