A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of $30$ turns and radius $12 \;cm .$ The coil is in a vertical plane making an angle of $45^{\circ}$ with the magnetic meridian. When the current in the coil is $0.35 \;A$, the needle points west to east.
$(a)$ Determine the horizontal component of the earth's magnetic field at the location.
$(b)$ The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of $90^{\circ}$ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.
A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of $30$ turns and radius $12 \;cm .$ The coil is in a vertical plane making an angle of $45^{\circ}$ with the magnetic meridian. When the current in the coil is $0.35 \;A$, the needle points west to east.
$(a)$ Determine the horizontal component of the earth's magnetic field at the location.
$(b)$ The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of $90^{\circ}$ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.
Number of turns in the circular coil, $N=30$
Radius of the circular coil, $r=12 \,cm =0.12 \,m$
Current in the coil, $I=0.35 \,A$
Angle of dip, $\delta=45^{\circ}$
$(a)$ The magnetic field due to current $I$, at a distance $r,$ is given as:
$B=\frac{\mu_{0} 2 \pi N T}{4 \pi r}$
Where,
$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7}\, T\,m \,A ^{-1}$
$\therefore B=\frac{4 \pi \times 10^{-7} \times 2 \pi \times 30 \times 0.35}{4 \pi \times 0.12}$
$=5.49 \times 10^{-5} \,T$
The compass needle points from West to East. Hence, the horizontal component of earth's magnetic field is given as
$B_{H}=B \sin \delta$
$=5.49 \times 10^{-5} \sin 45^{\circ}=3.88 \times 10^{-5} \,T =0.388 \,G$
$(b)$ When the current in the coil is reversed and the coil is rotated about its vertical axis by an angle of $90^{\circ},$ the needle will reverse its original direction. In this case, the needle will point from East to West.
Similar Questions
Assertion : In high latitudes one sees colourful curtains of light hanging down from high altitudes
Reason : The high energy charged particles from the sun are deflected to polar regions by the magnetic field of the earth.
Assertion : In high latitudes one sees colourful curtains of light hanging down from high altitudes
Reason : The high energy charged particles from the sun are deflected to polar regions by the magnetic field of the earth.
- [AIIMS 2003]
Tell the proper reason for the earth’s magnetic field to occur.
Tell the proper reason for the earth’s magnetic field to occur.
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 zero;
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 zero;
A bar magnet is situated on a table along east-west direction in the magnetic field of earth. The number of neutral points, where the magnetic field is zero, are
A bar magnet is situated on a table along east-west direction in the magnetic field of earth. The number of neutral points, where the magnetic field is zero, are
What is the angle between axis of rotation and magnetic axis of earth ?
What is the angle between axis of rotation and magnetic axis of earth ?