Question

A bar magnet of length 3cm has two points a and b along its axis at distances of 24 cm and 48 cm on opposite sides. Ratio of magnetic fields at these points will be

Answer 1

The ratio of magnetic fields at these points are 8:1

Explanation:

Given that

Length of magnet = 3 cm

Distance between point a and center of magnet= 24 cm

Distance between point b and center of magnet= 48 cm

The magnetic field is

$B=\dfrac{\mu_{0}\times 2m}{4\pi\times d^3}$

$B\propto\dfrac{1}{d^3}$

The magnetic field is inversely proportional to the cube of the distance.

We need to calculate the ratio of magnetic fields at these points

Using formula of magnetic field

$\dfrac{B_{a}}{B_{b}}=\dfrac{d_{b}^3}{d_{a}^2}$

$\dfrac{B_{a}}{B_{b}}=\dfrac{48^3}{24^3}$

$\dfrac{B_{a}}{B_{b}}=\dfrac{8}{1}$

Hence, The ratio of magnetic fields at these points are 8:1

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Topic : magnetic field

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