Exam 23: Electric Potential

Potential energy of a current loop: A round loop of diameter 12 cm, carrying a current of 0.40 A, is placed inside a magnetic field = 0.20 T + 0.40 T . The normal to the loop is parallel to the unit vector = -0.60 - 0.80 . What is the potential energy of the loop?

Force on currents: A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?

Direction of magnetic fields: A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points

Force on parallel wires: A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure). Which of the following statements is true?

Force on parallel wires: As shown in the figure, a rectangular current loop is carrying current = 3.0 A, in the direction shown, and is located near a long wire carrying a current . The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire, as shown. We measure that the net force on the rectangular loop is and is directed towards the wire. (a) What is the magnitude of the current I_w? (b) In which direction does I_w flow: from top to bottom or from bottom to top in the sketch?

Force on currents: A wire along the z-axis carries a current of 6.8 A in the +z direction. Find the magnitude and direction of the force exerted on a 6.1-cm long length of the wire by a uniform magnetic field with magnitude 0.36 T in the -x direction.

Ampere's law: A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ₀ = 4π × 10^-7 T ∙ m/A)

Force on currents: A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field. (a) Which way should the magnetic field point? (b) What is the magnitude of the weakest possible magnetic field you could use?

Field of a circular loop: Two circular coils of diameter 30.0 cm are parallel to each other and have their centers along the same line L but separated by 22.0 cm. When an experimenter views the coils along L, the coil closer to her carries a clockwise current of 2.50 A. Find the magnitude and sense (clockwise or counterclockwise) of the current needed in the other coil so that the net magnetic field on L midway between the two coils will have a magnitude of 4.10 µT and point away from the experimenter who is viewing the coils along L. (μ₀ = 4π × 10^-7 T ∙ m/A)

Cyclotron frequency: A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is

Force on moving charges: An electron moves with a speed of 8.0 × 10⁶ m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xy-plane. (1 eV = 1.60 × 10^-19 C, mel = 9.11 × 10^-31 kg) Calculate the magnitude of (a) the magnetic force on the electron. (b) the acceleration of the electron.

Solenoids: Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the length of the solenoid became twice as long (2L), and all other quantities remained the same, the magnetic field inside the solenoid would

Ampere's law: A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

Force on currents: An L-shaped metal machine part is made of two equal-length segments that are perpendicular to each other and carry a 4.50-A current as shown in the figure. This part has a total mass of 3.80 kg and a total length of 3.00 m, and it is in an external 1.20-T magnetic field that is oriented perpendicular to the plane of the part, as shown. What is the magnitude of the NET magnetic force that the field exerts on the part?

Torque: A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop?

Solenoids: A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ₀ = 4π × 10^-7 T ∙ m/A)

Force on parallel wires: The figure shows three long, parallel current-carrying wires. The magnitudes of the currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?

Field due to a long wire: The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact. The magnitude of the current is the same in all the wires, and the directions of current flow are as indicated. For which (if any) configuration will the magnetic field at the center of the square formed by the wires be equal to zero?

Force on moving charges: A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle.

Ampere's law: A very long, hollow, thin-walled conducting cylindrical shell (like a pipe) of radius R carries a current along its length uniformly distributed throughout the thin shell. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?