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 magnetic field.)

Solution

Here,
Current, I = 2.5 A.
Earth's magnetic field, B = 0.33G = 0.33 x 10^–4 T
Angle of dip, δ = 0°

Horizontal component of earth’s field
H = B cos δ
= 0.33 x 10^–4 cos 0°
= 0.33 x 10^–4 Tesla

Let the neutral points lie at a distance r from the cable.

Strength of magnetic field on this line due to
current in the cable $= \frac{μ_{0} I}{2 πr}$

At neutral point,
$\frac{μ_{0} I}{2 πr} = H \Rightarrow r = \frac{μ_{0} I}{2 πH} = \frac{4 π \times 10^{- 7} \times 2.5}{2 π \times 0.33 \times 10^{- 4}} = 1.5 \times 10^{- 2} m = 1.5 cm$

Hence, neutral points lie on a straight line parallel to the cable at a perpendicular distance of 1.5 cm above the plane of the paper.

Some More Questions From Magnetism and Matter Chapter

Answer the following question:
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?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

A bar magnet of magnetic moment 1.5 JT^–1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?
(b) What is the torque on the magnet in cases (i) and (ii)?

For Daily Free Study Material Join wiredfaculty

Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question:
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?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question: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?

Answer the following question:The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Answer the following question:
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?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?