Question

analyze the data to complete the statements.

• as distance from the magnet increases, the magnetic field strength
• ice from the magnet doubles from 3 cm to 6 cm, the

decreases ecomes as strong.
increases

Explanation:

First Statement:

Step1: Recall magnetic field behavior

Magnetic field strength \( B \) around a magnet follows an inverse - square law (for a dipole, \( B\propto\frac{1}{r^{2}} \), where \( r \) is the distance from the magnet). As \( r \) (distance) increases, \( B \) (magnetic field strength) decreases.

Step2: Determine the first blank

So, as distance from the magnet increases, the magnetic field strength decreases.

Second Statement:

Step1: Apply the inverse - square law

Let \( r_1 = 3\space cm \) and \( r_2=6\space cm \). The magnetic field strength \( B\propto\frac{1}{r^{2}} \). So, \( B_1\propto\frac{1}{r_1^{2}} \) and \( B_2\propto\frac{1}{r_2^{2}} \).

Step2: Find the ratio of \( B_2 \) to \( B_1 \)

\(\frac{B_2}{B_1}=\frac{\frac{1}{r_2^{2}}}{\frac{1}{r_1^{2}}}=\frac{r_1^{2}}{r_2^{2}}\). Substitute \( r_1 = 3 \) and \( r_2 = 6 \): \(\frac{3^{2}}{6^{2}}=\frac{9}{36}=\frac{1}{4}\). So when the distance doubles (from 3 cm to 6 cm), the magnetic field strength becomes \(\frac{1}{4}\) as strong.

Answer:

• As distance from the magnet increases, the magnetic field strength \(\boldsymbol{decreases}\).
• When the distance from the magnet doubles from 3 cm to 6 cm, the magnetic field strength becomes \(\boldsymbol{\frac{1}{4}}\) as strong.