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Ch 27: Magnetic Field and Magnetic Forces
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 27: Magnetic Field and Magnetic ForcesProblema 34a
Capitolo 27, Problema 34a

A straight, vertical wire carries a current of 2.60 A downward in a region between the poles of a large superconducting electromagnet, where the magnetic field has magnitude B = 0.588 T and is horizontal. What are the magnitude and direction of the magnetic force on a 1.00 cm section of the wire that is in this uniform magnetic field, if the magnetic field direction is (a) east?

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Identify the given values: The current I in the wire is 2.60 A, the magnetic field B is 0.588 T, and the length of the wire segment L is 1.00 cm (which is 0.01 m). The magnetic field direction is east, as shown in the image.
Use the formula for the magnetic force on a current-carrying wire: F = I * L * B * sin(θ), where θ is the angle between the direction of the current and the direction of the magnetic field.
Determine the angle θ: Since the current is downward and the magnetic field is horizontal towards the east, the angle between them is 90 degrees. Therefore, sin(θ) = sin(90°) = 1.
Substitute the values into the formula: F = 2.60 A * 0.01 m * 0.588 T * 1.
Determine the direction of the force using the right-hand rule: Point your thumb in the direction of the current (downward) and your fingers in the direction of the magnetic field (east). Your palm will face the direction of the force, which is towards the north.

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Magnetic Force on a Current-Carrying Wire

The magnetic force on a current-carrying wire in a magnetic field is given by the equation F = I * L * B * sin(θ), where I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the current direction and the magnetic field. This force is perpendicular to both the wire and the magnetic field.
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09:57
Magnetic Force on Current-Carrying Wire

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the magnetic force on a current-carrying wire. Point your thumb in the direction of the current and your fingers in the direction of the magnetic field; the force direction is perpendicular to both, indicated by the palm. In this scenario, with the current downward and the field east, the force is directed north.
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19:11
Force on Moving Charges & Right Hand Rule

Magnetic Field

A magnetic field is a vector field surrounding magnets and electric currents, characterized by the magnetic field strength B, measured in teslas (T). It exerts a force on moving charges and current-carrying wires. In this problem, the field is uniform and horizontal, affecting the wire section within its region, influencing the force direction and magnitude.
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05:30
Magnetic Fields and Magnetic Dipoles
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A straight, 2.5 m wire carries a typical household current of 1.5 A (in one direction) at a location where the earth's magnetic field is 0.55 gauss from south to north. Find the magnitude and direction of the force that our planet's magnetic field exerts on this wire if it is oriented so that the current in it is running (a) from west to east, (b) vertically upward, (c) from north to south. (d) Is the magnetic force ever large enough to cause significant effects under normal household conditions?

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Figure E27.49 shows a portion of a silver ribbon with z1 = 11.8 mm and y1 = 0.23 mm, carrying a current of 120 A in the +x-direction. The ribbon lies in a uniform magnetic field, in the y-direction, with magnitude 0.95 T. Apply the simplified model of the Hall effect presented in Section 27.9. If there are 5.85 x 1028 free electrons per cubic meter, find (a) the magnitude of the drift velocity of the electrons in the x-direction; (b) the magnitude and direction of the electric field in the z-direction due to the Hall effect; (c) the Hall emf.

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A long wire carrying 4.50 A of current makes two 90° bends, as shown in Fig. E27.35. The bent part of the wire passes through a uniform 0.240 T magnetic field directed as shown in the figure and confined to a limited region of space. Find the magnitude and direction of the force that the magnetic field exerts on the wire.

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