Question

Magnetic force _____ on increasing distance between the magnets.
A) Increases
B) Decreases
C) Remains Constant
D) May increase or decrease

Answer 1

Hint: We need to find the relation between the magnetic force or the magnetic field acting between two magnets and the distance between these magnets. We can use the Biot-Savart law to understand this and thereby solve the problem.

Complete answer:
We know that magnets produce magnetic fields which can be experienced by magnetic materials in its vicinity. A magnetic element such as current carrying wire produces a magnetic force on a magnetic object or another current carrying element. We know from the Biot-Savart’s law the strength of a magnetic field produced by a magnetic element is inversely dependent on the square of the distance of the magnet and the point under consideration.
i.e.,
\[B\propto \dfrac{1}{{{r}^{2}}}\]
Now, we know that the magnetic force experienced by a body is directly proportional to the magnetic field at the point. From this we can conclude that the magnetic force at a point is inversely proportional to the square of the distance, i.e.,
\[{{F}_{B}}\propto \dfrac{1}{{{r}^{2}}}\]
Now, we are given two magnets which are placed at a distance of R. We can apply the same condition and find the force acting on each of the magnets. The relation between the force between them and the distance between them can be given as –
\[{{F}_{B}}\propto \dfrac{1}{{{R}^{2}}}\]
So, we understand that the force between the magnets reduces by a factor of the square of the distance between them.

Therefore, the correct answer is option B.

Note:
The Biot-Savart’s law in magnetostatics is analogous to Coulomb's electrostatic force law. In both of them, the force is inversely proportional to the square of the distance between them and therefore, reduces with the increase in distance.