Exam 23: Electric Potential

Field of a circular loop: As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the z-axis. The wire carries a current of 8.0 A. What is the magnitude of the magnetic field at the origin? (μ₀ = 4π × 10^-7 T ∙ m/A)

Biot-Savart law: A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at point P, as the charge moves through the origin, is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ₀ = 4π × 10^-7 T ∙ m/A)

Force on moving charges: An electron, moving toward the west, enters a uniform magnetic field. Because of this field the electron curves upward. The direction of the magnetic field is

Circular motion of charges: A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle?

Force on currents: A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from points A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.75 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. What are the magnitude and direction of the force acting on (a) section AB of this wire? (b) section BC of this wire? (c) section CD of this wire? (d) section DE of this wire? (e) the entire wire?

Torque: A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium.

Ampere's law: A long, straight wire with current flowing through it produces magnetic field strength at its surface. If the wire has a radius R, where within the wire is the field strength equal to of the field strength at the surface of the wire? Assume that the current density is uniform throughout the wire. (μ₀ = 4π × 10^-7 T ∙ m/A)

Field of a circular loop: As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the x-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ₀ = 4π × 10^-7 T ∙ m/A)