Question

Two identical bar magnets of magnetic moment $M$ each, are placed along $X$ and $Y$ -axes, respectively at a distance $d$ from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on $X$ - axis and on the magnetic axis of magnet placed on $Y$ - axis. If the magnitude of total magnetic field at the origin is $B=\alpha \left[\frac{{\mu }_0}{4\pi }\frac{M}{d^3}\right]$, then the value of constant $\alpha$ will be $(d>>l$, where $l$ is the length of the bar magnets and direction of $N$ to $S$ in magnets is opposite with respect to each other)

• A. 2
• B. 1
• C. 3
• D. $\sqrt{5}$

Answer 1

Answer: (C)

Magnetic field due to axial magnet,
$B_1=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$ (+Y direction)
Magnetic field due to equatorial magnet,
$B_2=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$
$(+Y$ direction )
So, effective magnetic field
$B=B_1+B_2=3\frac{{\mu }_{0}M}{4\pi d^3}$
$\Rightarrow \alpha =3$