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

Question

A bar magnet of length 3 cm has points A and B along its axis at distances of 24 cm and 48 cm on the opposite sides. Ratio of magnetic field at the opposite sides. Ratio of magnetic fields at these points will be <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b211c20d901919d92874dc9b2ffb1b6d-.png" /> (A)  8  (B)  (1/2√2)  (C)  3  (D)  4

Tardigrade Admin · Accepted Answer

For a short magnet at a point along its axial line B=(μ0/4 π) ⋅ (2 M/r3) ⇒ (B1/B2)=((r2/r1))3=((48/24))3=(8/1)=8

Q. A bar magnet of length $3 c m$ has points $A$ and $B$ along its axis at distances of $24 c m$ and $48 c m$ on the opposite sides. Ratio of magnetic field at the opposite sides. Ratio of magnetic fields at these points will be

$8$

$\frac{1}{2 2}$

$3$

$4$

For a short magnet at a point along its axial line
$B = \frac{μ _{0}}{4 π} \cdot \frac{2 M}{r ^{3}}$
$\Rightarrow \frac{B _{1}}{B _{2}} = (\frac{r _{2}}{r _{1}})^{3} = (\frac{48}{24})^{3} = \frac{8}{1} = 8$

Q. A bar magnet of length 3cm has points A and B along its axis at distances of 24cm and 48cm on the opposite sides. Ratio of magnetic field at the opposite sides. Ratio of magnetic fields at these points will be

8

22​1​

3

4

For a short magnet at a point along its axial line B=4πμ0​​⋅r32M​ ⇒B2​B1​​=(r1​r2​​)3=(2448​)3=18​=8

Q. A bar magnet of length $3 c m$ has points $A$ and $B$ along its axis at distances of $24 c m$ and $48 c m$ on the opposite sides. Ratio of magnetic field at the opposite sides. Ratio of magnetic fields at these points will be

$8$

$\frac{1}{2 2}$

$3$

$4$

For a short magnet at a point along its axial line
$B = \frac{μ _{0}}{4 π} \cdot \frac{2 M}{r ^{3}}$
$\Rightarrow \frac{B _{1}}{B _{2}} = (\frac{r _{2}}{r _{1}})^{3} = (\frac{48}{24})^{3} = \frac{8}{1} = 8$