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प्रश्न
A long straight horizontal cable carries a current of 2.5 A in the direction 10° south of west to 10° north of east. The magnetic meridian of the place happens to be 10° 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.)
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उत्तर
Current in the wire, I = 2.5 A
Angle of dip at the given location on earth, δ = 0°
Earth’s magnetic field, H = 0.33 G = 0.33 × 10−4 T
The horizontal component of the earth’s magnetic field is given as:
HH = H cos δ
= 0.33 × 10−4 × cos 0°
= 0.33 × 10−4 T
The magnetic field at the neutral point at a distance R from the cable is given by the relation:
HH = `(μ_0"I")/(2π"R")`
Where,
μ0 = Permeability of free space = 4π × 10−7 T mA−1
∴ R = `(μ_0"I")/(2π"H"_"H")`
= `(4π xx 10^-7 xx 2.5)/(2π xx 0.33 xx 10^-4)`
= 15.15 × 10−3 m
= 1.51 m
Hence, a set of neutral points parallel to and above the cable are located at a normal distance of 1.51 cm.
संबंधित प्रश्न
The horizontal component of the earth’s magnetic field at a place is B and angle of dip is 60°. What is the value of vertical component of earth’s magnetic field at equator?
Name the electromagnetic waves which (i) maintain the Earth’s warmth and (ii) are used in aircraft navigation.
What is the angle of dip at a place where the horizontal and vertical components of the Earth’s magnetic field are equal?
Can the dip at a place be (a) zero (b) 90°?
What is a geographic meridian?
What happens to the angle of dip as we move towards magnetic pole from magnetic equator?
Answer the following question regarding earth’s magnetism:
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?
The earth’s magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?
A short bar magnet of magnetic moment 5.25 × 10−2 J T−1 is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45° with earth’s field on (a) its normal bisector and (b) its axis. Magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.
A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is 35°. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?
Which of the following statements about earth's magnetism is correct?
Which of the following is responsible for the earth’s magnetic field?
The horizontal component of earth’s magnetic field at a place is `sqrt3` times the vertical component. The angle of dip at that place is ______.
Assertion(A): A magnetic needle free to rotate in a vertical plane, orients itself (with its axis) vertical at the poles of the earth.
Reason (R): At the poles of the earth the horizontal component of earth’s magnetic field will be zero.
Select the most appropriate answer from the options given below:
The vertical component of earth's magnetic field is zero at a place where angle of dip is
At a place of latitude 5°, angle of dip is nearly
The earth's magnetic field at a certain place has a horizontal component 0.3 gauss and the total strength 0.5 gauss. The angle of dip is ______.
Isogonic lines are those for which ______.
