AIPMT PRELIMS 2004 Physics Electric Dipole MCQ Question

To understand the behavior of an electric dipole in a uniform electric field, let's first define what an electric dipole is. An electric dipole consists of two equal and opposite charges, $+q$ and $-q$, separated by a distance $d$. The dipole moment $p$ is defined as:

$$p = q \cdot d$$

1. Force on the Dipole:

When an electric dipole is placed in a uniform electric field $E$, the forces acting on the two charges are equal in magnitude but opposite in direction. The force $F$ on each charge due to the electric field is given by:

• Force on $+q$: $F_1 = +qE$
• Force on $-q$: $F_2 = -qE$

The net force $F_{net}$ on the dipole is the vector sum of these forces:

$$F_{net} = F_1 + F_2 = +qE - qE = 0$$

Thus, the total force acting on the dipole in a uniform electric field is zero.

2. Potential Energy of the Dipole:

The potential energy $U$ of an electric dipole in a uniform electric field is given by the formula:

$$U = -\vec{p} \cdot \vec{E}$$

When the dipole moment $p$ is aligned with the electric field $E$ (i.e., they are in the same direction), the angle between them is $0$ degrees. The cosine of $0$ degrees is $1$, so we have:

$$U = -pE \cos(0) = -pE$$

This indicates that the potential energy is at a minimum when the dipole moment is aligned with the electric field.

Conclusion:

Putting this all together, we find:

• The force on the dipole is zero.
• The potential energy is at its minimum.

Thus, the correct answer is B) zero and minimum.

3. Clarifying Incorrect Options:

• Option A (q E and p.E): This option incorrectly states that there is a force of $qE$, which is not true as shown above. The potential energy is also incorrectly given as $pE$ instead of $-pE$.

• Option C (q E and maximum): This option again incorrectly states the force as $qE$ (which is zero), and it also incorrectly suggests that the potential energy is at a maximum. The potential energy is minimum when aligned with the field, not maximum.

• Option D (2q E and minimum): This option incorrectly states the force as $2qE$, which does not reflect the physical situation as calculated. The potential energy being minimum is correct, but the force part is wrong.

In summary, the only correct interpretation of the system, given the conditions of the problem, is that the force on the dipole is zero, and its potential energy is at a minimum when the dipole moment is aligned with the electric field. Thus, option B is the right answer.