Question

A very long magnet is kept standing on its north pole at a distance $17.32cm$ from the center of the magnetic needle in the DMM arranged in tan A position. The deflection is ${30}^0$, when the magnet shifts to a position at a distance $10cm$ from the compass, the deflection is

• A. ${30}^0$
• B. ${60}^0$
• C. ${45}^0$
• D. ${90}^0$

Answer 1

The correct option is C ${45}^0$

In Tan A position
$B_H\tan \theta =\frac{2{\mu }_{0}M}{4\pi d^3}$
$\Rightarrow \tan \theta \propto \frac{1}{d^3}$
where, variables have their usual meanings.
Here, a very long magnet is kept standing on its north pole at a distance 17.32 cm from center of the magnetic needle in the DMM arranged in tan A position and the deflection is ${30}^{\circ }$ hence
$\tan {\theta }_1\propto \frac{1}{(17.32{)}^3}$ ...............(1)
and then the magnet shifts to a position at a distance 10cm from the compass on the same side hence,
$tan{\theta }_2\propto \frac{1}{(10{)}^3}$...............(2)
From (1) and (2) we can write
$\frac{tan{\theta }_2}{tan{\theta }_1}=\frac{(17.32{)}^3}{(10{)}^3}$
$tan{\theta }_2=1.732\times \tan 30$
$tan{\theta }_2=1.732\times 0.5773$
$tan{\theta }_2=0.9998\approx 1$
$\Rightarrow {\theta }_2={45}^{\circ }$