Question

The separation between two magnets is reduced by a factor of 5. How does the force between them change?

Answer 1

Answer:Increase by a factor of  25

Explanation:

We know that magnetic force is proportional to $\frac{1}{r^2}$

where r is the distance between them

$F\propto B\propto \frac{1}{r^2}$

Thus $F\propto \frac{1}{r^2}$

Where $B$=magnetic field

If distance is reduced by a factor of $5$ then force must increase by a factor of $25$ because

$r\rightarrow \frac{r}{5}$

so $F\propto \dfrac{1}{(\frac{r}{5})^2}$

$F\propto \frac{25}{r^2}$