Question

the images below show two pairs of magnets. the magnets in different pairs do not affect each other. all the magnets shown are made of the same material. pair 1 pair 2 think about the magnetic force between the magnets in each pair. which of the following statements is true? the magnitude of the magnetic force is greater in pair 1. the magnitude of the magnetic force is greater in pair 2. the magnitude of the magnetic force is the same in both pairs.

Explanation:

Step1: Determine the factors affecting magnetic force

The magnetic force between two magnets depends on the magnetic poles (whether they attract or repel) and the distance between them. Here, the distance between magnets in both pairs is the same ($41.9$ mm).

Step2: Analyze the nature of the force

For Pair 1: One magnet has its \(N\) - pole facing the other magnet's \(S\) - pole (opposite poles). Opposite poles attract.
For Pair 2: One magnet has its \(N\) - pole facing the other magnet's \(N\) - pole (like poles). Like poles repel. But the magnitude of the magnetic force (attraction or repulsion) between two magnets of the same material, same size and at the same distance depends only on the magnetic properties (which are same as they are of same material) and the distance (same here). The formula for the magnetic force between two magnetic dipoles (in a simple case) \(F\propto\frac{m_1m_2}{r^{2}}\), where \(m_1\) and \(m_2\) are magnetic moments (same for same - material magnets of same size) and \(r\) is the distance (same for both pairs).

Answer:

The magnitude of the magnetic force is the same in both pairs.