Two short bar magnets of magnetic moments $m$ each are arranged at the opposite corners of a square of side $d$ such that their centres coincide with the corners and their axes are parallel. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is
Two short bar magnets of magnetic moments $m$ each are arranged at the opposite corners of a square of side $d$ such that their centres coincide with the corners and their axes are parallel. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is
- A
$\frac{{{\mu _0}}}{{4\pi }}\frac{m}{{{d^3}}}$
- B
$\frac{{{\mu _0}}}{{4\pi }}\frac{{2m}}{{{d^3}}}$
- C
$\frac{{{\mu _0}}}{{4\pi }}\frac{m}{{2{d^3}}}$
- D
$\frac{{{\mu _0}}}{{4\pi }}\frac{{{m^3}}}{{2{d^3}}}$
Similar Questions
Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by
${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field
$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$
${{\rm{B}}_H} = $ Horizontal component of magnetic field
${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$
$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.
$(a)$ Find loci of points for which : dip angle is $ \pm $ $45^{°}$
Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by
${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field
$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$
${{\rm{B}}_H} = $ Horizontal component of magnetic field
${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$
$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.
$(a)$ Find loci of points for which : dip angle is $ \pm $ $45^{°}$
The angle of dip is the angle
The angle of dip is the angle
A very small magnet is placed in the magnetic meridian with its south pole pointing north. The null point is obtained $20\, cm $ away from the centre of the magnet. If the earth's magnetic field (horizontal component) at this point be $0.3$ $gauss$, the magnetic moment of the magnet is
A very small magnet is placed in the magnetic meridian with its south pole pointing north. The null point is obtained $20\, cm $ away from the centre of the magnet. If the earth's magnetic field (horizontal component) at this point be $0.3$ $gauss$, the magnetic moment of the magnet is
The values of the apparent angles of dip in two planes at right angles to each other are $45^{\circ}$ and $30^{\circ}$ respectively. The true value of angle of dip at the place is ............
The values of the apparent angles of dip in two planes at right angles to each other are $45^{\circ}$ and $30^{\circ}$ respectively. The true value of angle of dip at the place is ............
A compass needle whose magnetic moment is $60 \,amp × m^2$ pointing geographical north at a certain place, where the horizontal component of earth's magnetic field is $40\, \mu Wb/m^2$, experiences a torque $1.2 \times {10^{ - 3}}\,N \times m.$ What is the declination at this place......$^o$
A compass needle whose magnetic moment is $60 \,amp × m^2$ pointing geographical north at a certain place, where the horizontal component of earth's magnetic field is $40\, \mu Wb/m^2$, experiences a torque $1.2 \times {10^{ - 3}}\,N \times m.$ What is the declination at this place......$^o$