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Chapter 5: Problem 20

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

Expert verified
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

01

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.
02

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: \(W = \vec{F} \cdot \vec{d}\). 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
03

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.
04

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.

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Most popular questions from this chapter

A magnesium ion, Mg \(^{2+},\) with a charge of \(3.2 \times 10^{-19} \mathrm{Cand}\) an oxide ion, \(\mathrm{O}^{2-},\) with a charge of \(-3.2 \times 10^{-19} \mathrm{C}\) , are separated by a distance of 0.35 \(\mathrm{nm}\) . How much work would be required to increase the separation of the two ions to an infinite distance?

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