Exam 24: Magnetic Fields and Forces

A proton is accelerated from rest through 0.50 kV. It then enters a uniform magnetic field of 0.30 T that is oriented perpendicular to its direction of motion. (a) What is the radius of the path the proton follows in the magnetic field? (b) How long does it take the proton to make one complete circle in the magnetic field?.

A current-carrying loop of wire lies flat on a horizontal tabletop. When viewed from above, the current moves around the loop in a counterclockwise sense. For points on the tabletop inside the loop, the magnetic field lines caused by this current

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

A charged particle of mass 0.0040 kg is subjected to a $4.0 - T$ magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius $0.10 \mathrm {~m}$ at a speed of $2.0 \mathrm {~m} / \mathrm { s } \text {, }$ what is the magnitude of the charge on the particle?

A flat circular coil having 57 turns of very thin wire has a diameter of 9.5 cm and carries 7.2 A of current. (μ₀ = 4π × 10^-7 T ∙ m/A) (a) What is the strength of the magnetic field at the center of the coil? (b) If the same length of wire were used to make a coil with twice the original diameter, how large would the magnetic field at the center be when it carried the same current as before?

Two parallel straight wires are 7.0 cm apart and 50 m long. Each one carries a 18-A current in the same direction. One wire is securely anchored, and the other is attached in the center to a movable cart. If the force needed to move the wire when it is not attached to the cart is negligible, with what magnitude force does the wire pull on the cart? (μ₀ = 4π × 10^-7 T ∙ m/A)

Consider an ideal solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire windings. If the length of the solenoid becomes twice as long (to 2L), but all other quantities remained the same, the magnetic field inside the solenoid will

A proton, moving in a uniform magnetic field, moves in a circle perpendicular to the field lines and takes time T for each circle. If the proton's speed tripled, what would now be its time to go around each circle?

A single current-carrying circular loop of radius R is placed next to a long, straight wire, as shown in the figure. The current I in the wire flows to the right. In which direction must current flow in the loop to produce a net magnetic field of zero at its center?

The magnetic field at a distance of 2 cm from a long straight current-carrying wire is 4 μT. What is the magnetic field at a distance of 4 cm from this wire?

An electron moves with a speed of 3.0 × 10⁴ m/s perpendicular to a uniform magnetic field of 0.40 T. What is the magnitude of the magnetic force on the electron? (e = 1.60 × 10^-19C)

An electron is accelerated from rest through a potential difference of 3.75 kV. It enters a region where a uniform 4.0-mT magnetic field is perpendicular to the velocity of the electron. Calculate the radius of the path this electron will follow in the magnetic field. (e = 1.60 × 10^-19 C, m_electron = 9.11 × 10^-31 kg)

A flat circular loop of wire of radius 0.50 m that is carrying a 2.0-A current is in a uniform magnetic field of 0.30 T. What is the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field?

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 wire along the z-axis carries a current of 4.9 A in the +z direction. Find the magnitude and direction of the force exerted on a 3.3-cm long length of this wire by a uniform magnetic field pointing in the -x direction having a magnitude $0.43 \mathrm {~T}$

Consider an ideal solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire windings. If the radius of the solenoid is doubled to 2b, but all the other quantities remain the same, the magnetic field inside the solenoid will

At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is 0.10 mT. What current flows through the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

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

Two long parallel wires are placed side-by-side on a horizontal table. If the wires carry current in the same direction,

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