Question

A dipole is placed in an electric field and is allowed to come to equilibrium. How would the dipole react if the direction of the electric field is suddenly reversed? (A) $$ It rotates to align with the new field. (B) $$ It accelerates linearly along the field lines. (C) $$ It experiences no rotational or linear movement. (D) $$ It both rotates to align with the new field and accelerates linearly along the field lines.

Short answer

Option (A): It rotates to align with the new field.

Step-by-step solution

Understand the properties of a dipole in an electric field

A dipole consists of two equal and opposite charges separated by a small distance. When placed in an electric field, the positive charge experiences a force in the direction of the field, while the negative charge experiences a force in the opposite direction. This creates a torque that tends to align the dipole with the electric field.

Analyze the reaction to the reversed electric field

When the direction of the electric field is suddenly reversed, the alignment torque will act in the opposite direction. The dipole will rotate to align with the new direction of the electric field.

Determine if there's linear acceleration

While the dipole experiences a torque causing it to rotate, the forces on the individual charges are equal and opposite, so they cancel out in terms of linear motion. Therefore, there is no net force causing linear acceleration.

Choose the correct option

Given that the dipole rotates to align with the new field direction and does not experience linear acceleration, the correct answer is (A).

Key concepts

electric dipole

An electric dipole consists of two equal but opposite charges separated by a small distance. Think of a simple molecule like water, where one side is slightly positive, and the other is slightly negative. The positive charge is typically denoted as +q and the negative charge as -q. This separation of charges creates a dipole moment ($\mathbf{\text{p}}$), which is a vector quantity pointing from the negative to the positive charge. The dipole moment is given by the product of one of the charges and the distance ($d$) between them, i.e., $\mathbf{\text{p}}=q\times d$. Dipoles are key to understanding interactions between charged particles in fields.

electric field

An electric field ($\mathbf{\text{E}}$) is a field around charged particles that exerts force on other charges within the field. This is described mathematically as the force ($\mathbf{\text{F}}$) per unit charge ($q$), $\mathbf{\text{E}}=\frac{\mathbf{\text{F}}}{q}$. Electric fields are created by electric charges, and they can be visualized using field lines that indicate the direction and strength of the field. When a dipole is placed in an electric field, the positive and negative charges experience forces in opposite directions because they are of opposite signs. This interaction affects the dipole's behavior in the field.

torque on dipole

When a dipole is in an electric field, the electric forces on the positive and negative charges create a torque ($\tau$). This torque results in a rotational force attempting to align the dipole with the electric field direction. The torque ($\tau$) on a dipole in a uniform electric field is calculated as the cross product of the dipole moment ($\mathbf{\text{p}}$) and the electric field ($\mathbf{\text{E}}$), $\tau =\mathbf{\text{p}}\times \mathbf{\text{E}}$. The maximum torque occurs when the dipole is perpendicular to the electric field. As the dipole rotates towards alignment, the torque decreases until it becomes zero when the dipole is parallel to the field.

dipole alignment

Dipole alignment in an electric field is the process by which a dipole rotates to align its dipole moment with the direction of the electric field. Initially, the dipole experiences torque that starts this rotation. Over time, the rotational motion slows as the dipole gets closer to alignment. When the electric field direction is suddenly reversed, the dipole moment will again experience torque but this time in the opposite direction, causing it to rotate until it aligns with the new field direction. It's important to note that while rotational movement occurs, the forces on the dipole's charges cancel out in terms of linear motion, preventing any linear acceleration. Therefore, given such a scenario, the dipole rotates but doesn’t move linearly.