Magnetic induction
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1.Explain the physical quantity “stationary magnetic field” and its characteristics.
Solution:
A stationary magnetic field is a time-invariant, constant magnetic field. It arises around a stationary permanent magnet or around a stationary conductor carrying a constant electric current. It is represented by magnetic induction lines (MIL).
2.A conductor placed in a homogeneous stationary magnetic field perpendicular to the direction of induction lines with an active length of 5 cm carries a current of 25 A. The magnetic field exerts a force of 50 mN on the conductor. Determine the magnitude of the magnetic induction.
Solution:
Analysis:
The magnetic induction of the field is B = 40 mT
3.A straight conductor of length 10 cm carrying a current of 2 A is acted upon by a force of 20 mN in a homogeneous magnetic field with magnetic induction of 0.2 T. Determine the angle between the conductor and the direction of the magnetic induction lines.
Solution:
Analysis:
The angle between the conductor and the direction of the magnetic induction lines is 300.
4.A conductor carrying a current of 1 A with a cross-sectional area of 1 mm2 moves in a homogeneous magnetic field with constant acceleration of 2 m·s–2 perpendicular to the direction of induction lines. The density of the material of the conductor is 2500 kg·m3. Determine the magnitude of the magnetic induction.
Solution:
Analysis:
The magnitude of magnetic induction is B = 5 mT.
5.A straight conductor forming an angle α1 = 900 with the induction lines of a homogeneous magnetic field experiences a force greater by 0.134 N than when it formed an angle α2 = 600. Determine the magnetic induction of the field if the effective length of the conductor is l = 12.5 cm and it carries a current of 10 A.
Solution:
Analysis:
The magnetic induction of the field is B = 0.8 T.
6.What electric current flows through a very long straight conductor if the magnetic induction at a distance of 20 cm from the conductor is 20 μT?
Solution:
Analysis:
The very long straight conductor carries a current of I = 20 A.
7.What magnetic induction does the magnetic field of a solenoid of length 20 cm with 400 turns have, if the current passing through the solenoid is 5 A? What is the diameter of the wire from which the solenoid is wound, if the single-layer winding has turns placed directly next to each other?
Solution:
Analysis:
- The magnetic field of the solenoid has a magnetic induction B = 4π·10-3 T.
- The diameter of the wire is d = 0.1 mm.
8.A straight conductor with current I formed an angle α with the induction lines of a homogeneous magnetic field. After changing its position, the conductor forms an angle α + 180 with the induction lines. The magnitude of the force acting on the conductor increased by 20%. Determine the angle α.
Solution:
Analysis:
The angle α = 510.
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