Advertisements
Advertisements
प्रश्न
Solve the following problem.
A magnet makes an angle of 45° with the horizontal in a plane making an angle of 30° with the magnetic meridian. Find the true value of the dip angle at the place.
Advertisements
उत्तर
Let the true value of dip be Φ. When the magnet is kept 45° aligned with declination 30°, the horizontal component of Earth’s magnetic field.
B’H = BH cos 30° Whereas, the vertical component remains unchanged.
∴ For an apparent dip of 45°,
tan 45° = `"B"_"V"^′/"B"_"H"^′="B"_"V"/("B"_"H"cos30°)="B"_"V"/"B"_"H"xx1/(cos30°)`
But, real value of dip is,
tan Φ = `"B"_"V"/"B"_"H"`
∴ tan 45° = `tanΦ/(cos30°)`
∴ tan Φ = tan 45° × cos 30°
= `1xxsqrt3/2`
∴ Φ = tan−1 (0.866)
The true value of angle of dip is tan−1 (0.866).
APPEARS IN
संबंधित प्रश्न
Name three elements of the earth's magnetic field which help in defining earth's magnetic field completely.
A compass needle, free to turn in a vertical plane orients itself with its axis vertical at a certain place on the earth. Find out the values of (i) horizontal component of earth's magnetic field and (ii) angle of dip at the place.
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?
Where on the surface of Earth is the angle of dip zero?
A horizontal straight wire of length L extending from east to west is falling with speed v at right angles to the horizontal component of Earth’s magnetic field B.
(i) Write the expression for the instantaneous value of the e.m.f. induced in the wire.
(ii) What is the direction of the e.m.f.?
(iii) Which end of the wire is at the higher potential?
Can the earth's magnetic field be vertical at a place? What will happen to a freely suspended magnet at such a place? What is the value of dip here?
The reduction factor K of a tangent galvanometer is written on the instrument. The manual says that the current is obtained by multiplying this factor to tan θ. The procedure works well at Bhuwaneshwar. Will the procedure work if the instrument is taken to Nepal? If there is same error, can it be corrected by correcting the manual or the instrument will have to be taken back to the factory?
What is the angle of dip at a place where the horizontal component `(B_H)` and vertical component `(B_V)` of earth’s magnetic field are equal :
The horizontal component of the earth's magnetic field at a place is `1/sqrt(3)` time the vertical component. Determine the angle of dip at that place.
Answer the following question regarding earth’s magnetism:
A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field.
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?
Answer the following question regarding earth’s magnetism:
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?
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth’s field in such distant past?
Interstellar space has an extremely weak magnetic field of the order of 10–12 T. Can such a weak field be of any significant consequence? Explain.
A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 22° with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earth’s magnetic field at the place.
At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. Specify the direction and magnitude of the earth’s field at the location.
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.
Which of the following statements about earth's magnetism is correct?
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 Gauss, and the angle of dip is zero. Locate the line of neutral points. (Ignore the thickness of the cable).
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,
A 10-meter wire is kept in east-west direction. It is falling down with a speed of 5.0 meter/second, perpendicular to the horizontal component of earth's magnetic field of 0.30 × 10−4 weber/meter2. The momentary potential difference induced between the ends of the wire will be:
The angle between the magnetic meridian and geographical meridian is called ______
Let the magnetic field on earth be modelled by that of a point magnetic dipole at the centre of earth. The angle of dip at a point on the geographical equator ______.
- is always zero.
- can be zero at specific points.
- can be positive or negative.
- is bounded.
Assume the dipole model for earth’s magnetic field B which is given by BV = vertical component of magnetic field = `mu_0/(4pi) (2m cos theta)/r^3` BH = Horizontal component of magnetic field = `mu_0/(4pi) (sin theta m)/r^3` θ = 90° – lattitude as measured from magnetic equator. Find loci of points for which (i) |B| is minimum; (ii) dip angle is zero and (iii) dip angle is ± 45°.
The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to 8 × 1022 Am2, the value of earth's magnetic field near the equator is close to ______. (radius of the earth = 6.4 × 106 m)
