Advertisements
Advertisements
Question
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° 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° in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.
Solution
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, δ = 45°
(a) The magnetic field due to current I, at a distance r, is given as:
B = `(μ_0 2π"NI")/(4π"r")`
Where,
μ0 = Permeability of free space = 4π × 10−7 T mA−1
∴ B = `(4π xx 10^-7 xx 2π xx 30 xx 0.35)/(4π xx 0.12)`
= 5.49 × 10−5 T
The compass needle points from West to East. Hence, the horizontal component of the earth’s magnetic field is given as:
BH = B sin δ
= 5.49 × 10−5 sin 45°
= 3.88 × 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 º, the needle will reverse its original direction. In this case, the needle will point from East to West.
APPEARS IN
RELATED QUESTIONS
Choose the correct answer from given options
A charge particle after being accelerated through a potential difference 'V' enters in a uniform magnetic field and moves in a circle of radius r. If V is doubled, the radius of the circle will become
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:
The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 × 1022 J T−1 located at its centre. Check the order of magnitude of this number in some way.
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 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.)
The angle of dip at a certain place where the horizontal and vertical components of the earth’s magnetic field are equal is ______.
At a given place on earth’s surface the horizontal component of earth’s magnetic field is 2 × 103-5 T and resultant magnetic field is 4 × 103-5 T. The angle of dip at this place is ______.
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,
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.
