A long straight horizontal cable carries a current of $2.5\;A$ in the direction $10^{\circ}$ south of west to $10^{\circ}$ north of east. The magnetic meridian of the place happens to be $10^{\circ}$ west of the geographic meridian. The earth's magnetic field at the location is $0.33\; G ,$ and the angle of $dip$ is zero. Locate the line of neutral points (ignore the thickness of the cable)? (At neutral points, magnetic field due to a current-carrying cable is equal and opposite to the horizontal component of earth's magnetic field.)
A long straight horizontal cable carries a current of $2.5\;A$ in the direction $10^{\circ}$ south of west to $10^{\circ}$ north of east. The magnetic meridian of the place happens to be $10^{\circ}$ west of the geographic meridian. The earth's magnetic field at the location is $0.33\; G ,$ and the angle of $dip$ is zero. Locate the line of neutral points (ignore the thickness of the cable)? (At neutral points, magnetic field due to a current-carrying cable is equal and opposite to the horizontal component of earth's magnetic field.)
Current in the wire, $I=2.5 \,A$
Angle of dip at the given location on earth, $\delta=0^{\circ}$
Earth's magnetic field, $H=0.33\, G=0.33 \times 10^{-4} \,T$
The horizontal component of earth's magnetic field is given as:
$H_{H}=H \cos \delta$
$=0.33 \times 10^{-4} \times \cos 0^{\circ}=0.33 \times 10^{-4} \,T$
The magnetic field at the neutral point at a distance $R$ from the cable is given by the relation:
$H_{H}=\frac{\mu_{0} I}{2 \pi R}$
Where,
$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \,T\,m\, A ^{-1}$
$\therefore R=\frac{\mu_{0} I}{2 \pi H_{H}}$
$=\frac{4 \pi \times 10^{-7} \times 2.5}{2 \pi \times 0.33 \times 10^{-4}}$$=15.15 \times 10^{-3} \,m =1.51 \,cm$
Hence, a set of neutral points lie on a straight line parallel to the cable at a perpendicular distance of $1.51\, cm ,$ above the plane of the paper.
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- [KVPY 2021]
Answer the following questions regarding earth’s magnetism:
$(a)$ A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field.
$(b)$ The angle of dip at a location in southern India is about $18^o$. Would you expect a greater or smaller dip angle in Britain?
$(c)$ If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?
$(d)$ In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?
$(e)$ The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment $8 \times 10^{22}\; J\, T^{-1}$ located at its centre. Check the order of magnitude of this number in some way.
$(f)$ Geologists claim that besides the main magnetic $N-S$ poles, there are several local poles on the earth’s surface oriented in different directions. How is such a thing possible at all?
Answer the following questions regarding earth’s magnetism:
$(a)$ A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field.
$(b)$ The angle of dip at a location in southern India is about $18^o$. Would you expect a greater or smaller dip angle in Britain?
$(c)$ If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?
$(d)$ In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?
$(e)$ The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment $8 \times 10^{22}\; J\, T^{-1}$ located at its centre. Check the order of magnitude of this number in some way.
$(f)$ Geologists claim that besides the main magnetic $N-S$ poles, there are several local poles on the earth’s surface oriented in different directions. How is such a thing possible at all?
Tell the proper reason for the earth’s magnetic field to occur.
Tell the proper reason for the earth’s magnetic field to occur.