Chapter 7, Problem 41R

To determine

Whether the magnetic field strength decreases more rapidly with distance closer to the wire or farther from the wire.

Explanation of Solution

Given:

Consider the graph of magnetic field strength vs distance from wire provided in the question.

In the given graph, the smallest division along x-axis is $\text{1 cm}$ and that along y-axis is $\text{4 μT}$ .

The graph shows that magnetic field strength decreases with increase in distance from the wire.

From the nature of the graph, it can be predicted that magnetic field strength decreases more rapidly with distance closer to the wire. At $\text{1 cm}$ from the wire the magnetic field strength is $20\text{ μT}$ , but at $\text{2 cm}$ it has decreased rapidly to about $10\text{ μT}$ , that is, in $\text{1 cm}$ increase the field strength has decreased by $10\text{ μT}$ . Now, at $\text{3 cm}$ from the wire the magnetic field strength is about $6.5\text{ μT}$ . So, on increase in $\text{1 cm}$ distance, the magnetic field strength has decreased only by $3.5\text{ μT}$ . Further, on a change of $\text{1 cm}$ , from $\text{5 cm}$ to $\text{6 cm}$ , the magnetic field strength decreases only by about $0.5\text{ μT}$ .Thus, as we go farther away from the wire the field strength decreases slowly. At a distance closer to the wire, the field strength decreases rapidly.

Conclusion: The magnetic field strength decreases more rapidly with distance closer to the wire