Question

The magnetic field strength at a point at a distance d from the centre on the axial line of a very short bar magnet of Magnetic moment $M$ is $B$. The Magnetic induction at a distance $2d$ from the centre on the equatorial line of a Magnetic Moment $8M$ will be

• A. $4B$
• B. $0.25B$
• C. $0.5B$
• D. $2B$

Answer 1

The correct option is C $0.5B$

$B_{axial}=\frac{2{\mu }_{0}m}{4\pi d^3}$
$B_{equatorial}=\frac{{\mu }_{0}m}{4\pi d^3}$
$d_1=d$
$d_2=2d$
Also,
$m_1=M$
$m_2=8M$

$B_1=\frac{2{\mu }_{0}m}{4\pi d^3}............1$

$B_2=\frac{2{\mu }_{0}m}{4\pi d^3}=\frac{{\mu }_{0}8M}{4\pi (2d{)}^3}.........2$
From 1 & 2 we get that,
$B_{equatorial}=\frac{B}{2}$