Exam 24: Magnetic Fields and Forces

Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions. What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ₀ = 4π × 10^-7 T ∙ m/A)

A circular metal loop of radius 10 cm and three long straight wires carry currents of $I _ { 1 } = 20 \mathrm {~A} ,$ $I _ { 2 } = 50 \mathrm {~A} ,$ $I _ { 3 } = 20 \mathrm {~A} ,$ and $I _ { 4 } = 40 \mathrm {~A} ,$ as shown in the figure. Each of the straight wires is 20 cm from the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper. What is the y component of the resultant magnetic field at the center of the loop? (?₀ = 4? × 10^-7 T ? m/A)

In the figure, a rectangular current loop is carrying current I₁ = 7.0 A, in the direction indicated, near a long wire carrying a current I_w. 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. If the net force on the loop is to have magnitude $1.7 \times 10 ^ { - 6 } \mathrm {~N}$ and is to be directed towards the wire, what must be the magnitude and direction (from top to bottom or from bottom to top in the sketch)of the current I_w in the wire? (?₀ = 4? × 10^-7 T ? m/A)

A proton, with mass 1.67 × 10^-27 kg and charge +1.6 × 10^-19 C, is sent with velocity $2.3 \times 10 ^ { 4 } \mathrm {~m} / \mathrm { s }$ in the +x direction into a region where there is a uniform electric field of magnitude $780 \mathrm {~V} / \mathrm { m }$ in the +y direction. What must be the magnitude and direction of the uniform magnetic field in the region if the proton is to pass through undeflected? Assume that the magnetic field has no x component and neglect gravitational effects.

Two long, parallel wires carry currents of different magnitudes. If the amount of current in one of the wires is doubled, what happens to the magnitude of the force that each wire exerts on the other?

A flat square coil of wire measures 9.5 cm on each side and contains 175 turns of very thin wire. It carries a current of 6.3 A in a uniform 0.84-T magnetic field. What angle less than 90° should the plane of this coil make with the magnetic field direction so that the magnitude of the magnetic torque on it is 6.5 N ? m?

A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. -The loop rotates in the magnetic field and at one point the plane of the loop is parallel to the field. At that instant, what is the magnitude of the torque acting on the wire due to the magnetic field?

An electron has an initial velocity to the south but is observed to curve upward as the result of a magnetic field. This magnetic field must have a component

A charged particle is injected into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field lines. Ignoring the particle's weight, the particle will

A proton, moving west, enters a magnetic field. Because of this magnetic field the proton curves upward. We may conclude that the magnetic field must have a component

A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? (μ₀ = 4π × 10^-7 T ∙ m/A)

A negatively charged particle -Q is moving to the right, directly above a wire having a current I flowing to the right, as shown in the figure. In what direction is the magnetic force exerted on the particle due to the current?

A flat circular coil has 250 identical loops of very thin wire. Each loop has an area of 0.12 m² and carries 15 mA of current. This coil is placed in a magnetic field of 0.050 T oriented at 30° to the plane of the loop. What is the magnitude of the magnetic moment of the coil?

A positive charge is moving to the right and experiences an upward magnetic force, as shown in the figure. In which direction must the magnetic field have a component?

After landing on an unexplored Klingon planet, Spock tests for the direction of the magnetic field by firing a beam of electrons in various directions and by recording the following observations: Electrons moving upward feel a magnetic force in the northwest direction. Electrons moving horizontally toward the north are pushed downward. Electrons moving horizontally toward the southeast are pushed upward. Mr. Spock therefore concludes that the magnetic field at this landing site is in which direction?

What is the force per meter on a straight wire carrying 5.0 A when it is placed in a magnetic field of 0.020 T so that the wire makes an angle of 27° with respect to the magnetic field lines.

A flat circular wire loop lies in a horizontal plane on a table and carries current in a counterclockwise direction when viewed from above. At this point, the earth's magnetic field points to the north and dips below the horizontal. Which side of the coil tends to lift off of the table due to the magnetic torque on the loop?

In the figure, a small particle of charge -1.9 x $10 ^ { - 6 }$ C and mass $m = 3.1 \times 10 ^ { - 12 } \mathrm {~kg}$ has speed $10 = 8.1 \times 10 ^ { 3 } \mathrm {~m} / \mathrm { s }$ as it enters a region of uniform magnetic field. The particle is initially traveling perpendicular to the magnetic field and is observed to travel in the semicircular path shown with radius R = 5.0 cm. Find the magnitude and direction of the magnetic field in the region.

A proton has an initial velocity to the south but is observed to curve upward as the result of a magnetic field. This magnetic field must have a component

A straight wire carries a current of 10 A at an angle of 30° with respect to the direction of a uniform 0.30-T magnetic field. Find the magnitude of the magnetic force on a 0.50-m length of the wire.