Question

A bar magnet is placed with its north pole pointing towards north. The neutral point is at a distance $20cm$ from the center of the magnet. The net magnetic induction at a distance $10cm$ on the axial line of the magnet is:

• A. $3B_H$
• B. $7B_H$
• C. $15B_H$
• D. $17B_H$

Answer 1

The correct option is B $7B_H$

$B_H=\frac{2{\mu }_{0}M}{4\pi d^3}$ (At Nullpoint) d=20m
$B_H=\frac{2{\mu }_{0}M}{4\pi (20{)}^3}$
as $B\propto \frac{1}{d^3}$
$\frac{B_{20cm}}{B_{10cm}}=\frac{{10}^3}{{20}^3}$
$\Rightarrow B_{10cm}=8B_{20cm}=8B_H$
At 10cm from the magnet,
$B=B_{magnet}-B_H$
$=8B_H-B_H$
$=7B_H$