Question

Identify the force present and explain whether work is done when (a) a positively charged particle moves in a circle at a fixed distance from a negatively charged particle, (b) an iron nail is pulled off a magnet.

Short answer

In situation (a), the force involved is the Coulomb force between the positively and negatively charged particles. However, no work is done as the displacement of the positively charged particle is always perpendicular to the force acting on it. In situation (b), the force involved is the magnetic force between the iron nail and the magnet. Work is done when pulling the iron nail off the magnet because the angle between the external force applied and the displacement of the nail is 0 degrees, resulting in a non-zero dot product.

Step-by-step solution

Identify the force involved

The force involved in this situation is the electrostatic force between the positively charged particle and the negatively charged particle, which is also known as the Coulomb force. This force is always attractive since the charged particles have opposite charges.

Determine whether work is done

To determine if work is done, we need to consider the definition of work in physics. Work (W) is defined as the dot product of the force (F) acting on a particle and the displacement (d) of the particle: $W=\overrightarrow{F}\cdot \overrightarrow{d}$. If the angle between the force and the displacement is 90 degrees, the dot product becomes zero and no work is done. In this case, the positively charged particle is moving in a circle around the negatively charged particle, meaning its displacement is always perpendicular to the force acting on it (Coulomb force). Since the angle between the force and the displacement is 90 degrees, the dot product is zero, and no work is done. Situation (b): Pulling an iron nail off a magnet

Identify the force involved

The force involved in this situation is the magnetic force between the iron nail and the magnet. This force is attractive, keeping the nail attached to the magnet.

Determine whether work is done

In order to remove the nail from the magnet, an external force must be applied to the nail in the opposite direction of the magnetic force. When this external force is applied, the displacement of the nail is away from the magnet and in the same direction as the external force. Since the angle between the external force and displacement is 0 degrees, the dot product of the force and displacement is non-zero and work is done. In summary, (a) no work is done as the positively charged particle moves in a circle around the negatively charged particle, and (b) work is done when pulling the iron nail off the magnet.

Key concepts

Understanding Electrostatic Force

Electrostatic force is what causes charged objects to attract or repel each other. It occurs between charged particles like electrons and protons. In our exercise, a positively charged particle is influenced by a negatively charged one.
This force is fundamental in nature and is responsible for holding atoms together.

• Opposite charges: Attract each other, creating an attractive force.
• Like charges: Repel each other, resulting in a repulsive force.

The strength of this force depends on the amount of charge and the distance between them. As the distance increases, the force decreases.

Exploring Coulomb's Law

Coulomb's Law helps us calculate the electrostatic force between two charge particles. This law states that the force (F) between charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula is expressed as:
$$F=\frac{k\cdot |q_1\cdot q_2|}{r^2}$$
where:

• F = electrostatic force
• k = Coulomb's constant (8.99 \times 10^9 \mathrm{Nm^2/C^2})
• q_1 and q_2 = charges
• r = distance between charges

Using this law, we can predict how strong the force is based on distance and charge. It helps explain why a positively charged particle experiences force towards a negatively charged one.

Delving into Magnetic Force

Magnetic forces are attractive or repulsive forces that occur due to magnetic fields. In the scenario with the iron nail and magnet, the magnetic force keeps the nail attached.

• Magnetic fields: Created by magnets or moving charges.
• Iron and magnets: Attract each other, leading to an adhesive force.

When you pull the nail off, you apply an external force. The nail moves in the direction of this force, hence work is done because the force and displacement are aligned.

Understanding the Concept of Work in Physics

In physics, work is done when a force causes an object to move in the direction of the force. The key here is the relationship between force and displacement.
The formula for work (W) is:
$$W=\overrightarrow{F}\cdot \overrightarrow{d}$$
Here, work involves the dot product of force and displacement:

• Parallel force and displacement: Work is maximized as the angle is 0 degrees.
• Perpendicular force and displacement: No work is done as the angle is 90 degrees.

For the particle moving in a circle, force and displacement are always perpendicular, hence no work. In removing the nail, the force aligns with displacement, resulting in work being done.