Question

9. When considering a magnet's force of attraction over a known distance, you would expect the strength of attraction 4 inches away from the magnet to be _______ weaker than the strength of attraction at 1 inch from the magnet.
A. 6 times
B. 16 times
C. 4 times
D. 8 times

Answer 1

Answer: B. 16 times

Explanation:

The mathematic expression for a magnetic force $F_{M}$ between two magnets is:

$F_{M}=K_{M}\frac{m_{1}m_{2}}{r^{2}}$   (1)

Where:

$K_{M}$ is a constant

${m_{1}$ and ${m_{2}$ are the magnetic charges, which depends on the size of each magnet

$r$ is the distance beteween both magnets

As we can see, this force in inversely proportional to the square of the distance. This means that if we increase the distance, the magnetic force will decrease.

Now, if we increase this value by 4 inches from 1 inch:

$F_{M}=K_{M}\frac{m_{1}m_{2}}{{(4)}^{2}}$   (2)

$F_{M}=K_{M}\frac{m_{1}m_{2}}{16}$   (3)

This means the strength of attraction will be 16 times weaker.