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Physics-

General

Easy

Question

Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance $d$ from the center on the bisector of the right angle is

$\frac{μ_{0}}{4 π} \frac{2 \sqrt{2} M}{d^{3}}$
$\frac{μ_{0}}{4 π} \frac{2 M}{d^{3}}$
$\frac{μ_{0}}{4 π} \frac{M}{d^{3}}$
$\frac{μ_{0}}{4 π} \frac{2 \sqrt{2} M}{d^{3}}$

The correct answer is: $fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 square root of 2 M over denominator d to the power of 3 end exponent end fraction$

Resolving the magnetic moments along $O P$ and perpendicular to $O P comma$ figure we find that component $O P$ perpendicular $O P$ cancel out. Resultant magnetic moment along $O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree$

$equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M$
The point $P$ lies on axial line of magnet of moment
$equals square root of 2 M$
$therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction$

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