Exercises: Magnetic Fields, Field Lines, and Force

Which statement best distinguishes a magnetic field from an electric field?

Which of the following is NOT a source of a magnetic field?

A student draws magnetic field lines for a bar magnet and makes one of the following errors. Which rule for magnetic field lines did the student violate?

The student draws field lines that cross each other near the north pole.

A bar magnet's magnetic field strength is $B = 0.1\ \text{T}$ near its pole. The SI unit of magnetic field strength is the tesla. Which statement correctly relates the tesla to base SI units?

A proton ($q = +e$) moves to the right (in the $+x$ direction) through a magnetic field pointing upward (in the $+y$ direction). Using the force right-hand rule (fingers along $v$, curl toward $B$, thumb gives $F$), what is the direction of the magnetic force on the proton?

A current-carrying wire lies along the $x$-axis with current flowing in the $+x$ direction (to the right). A uniform magnetic field $\mathbf{B}$ points in the $+y$ direction (upward). Using the force right-hand rule for a wire (fingers along current, curl toward $B$, thumb gives $F$), what is the direction of the magnetic force on the wire?

An electron ($q = 1.6 \times 10^{-19}\ \text{C}$, charge magnitude) moves at $v = 3.0 \times 10^6\ \text{m/s}$ perpendicular to a magnetic field of $B = 0.050\ \text{T}$. Calculate the magnitude of the magnetic force on the electron in newtons. The velocity is perpendicular to the field ($\theta = 90\degree$).

A wire of length $L = 0.30\ \text{m}$ carries a current of $I = 5.0\ \text{A}$ and is placed perpendicular ($\theta = 90\degree$) to a uniform magnetic field $B = 0.40\ \text{T}$. Calculate the magnitude of the force on the wire in newtons.

A straight wire of length $L = 0.50\ \text{m}$ carries $I = 2.0\ \text{A}$ at an angle of $\theta = 30\degree$ to a magnetic field of $B = 0.20\ \text{T}$. Calculate the magnitude of the force on the wire in newtons.

A student draws a bar magnet field line diagram. Which of the following descriptions correctly represents the field lines outside the magnet?

Complete the statement about magnetic force magnitude:

The force on a charge $q$ moving at speed $v$ in a field $B$ is $F = qvB \times \_\_\_$, which equals   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   when the charge moves parallel to the field, and   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   when the charge moves perpendicular to the field.

An alpha particle ($q = +2e$, positive charge) moves into the page. A magnetic field $\mathbf{B}$ points to the right. Using the right-hand rule, what is the direction of the magnetic force on the alpha particle?

Two parallel wires carry currents in opposite directions — wire A carries current to the right and wire B carries current to the left. What is the magnetic force between them?

A proton moves in a circular path at constant speed inside a uniform magnetic field. Which statement correctly explains this motion?

A cosmic ray proton ($q = 1.6 \times 10^{-19}\ \text{C}$) traveling at $v = 2.0 \times 10^7\ \text{m/s}$ enters Earth's magnetic field at an angle of $\theta = 60\degree$ to the field lines. Earth's field strength is $B = 5.0 \times 10^{-5}\ \text{T}$.

Calculate the magnitude of the magnetic force on the proton in newtons. Express your answer in scientific notation.

A galvanometer uses the force on a current-carrying coil in a magnetic field to deflect a needle. The coil has $N = 200$ turns, each of effective length $L = 0.025\ \text{m}$. The magnetic field is $B = 0.15\ \text{T}$ and the coil carries a current of $I = 0.50\ \text{mA}$ ($0.50 \times 10^{-3}\ \text{A}$). All wires are perpendicular to the field.

Calculate the total magnetic force on all turns of the coil combined, in newtons.

What error did the student make in describing the right-hand rule?

What is the fundamental error in this calculation?

A proton ($m = 1.67 \times 10^{-27}\ \text{kg}$, $q = 1.6 \times 10^{-19}\ \text{C}$) moves perpendicular to a uniform magnetic field $B = 0.30\ \text{T}$ and follows a circular path. The centripetal force equals the magnetic force: $mv^2/r = qvB$.

If the proton's speed is $v = 4.0 \times 10^6\ \text{m/s}$, calculate the radius of the circular orbit in meters. Round to two significant figures.

Explain why a magnetic field can change the direction of a moving charged particle but cannot change its speed. In your explanation, use the concept of work and the relationship between force and velocity direction.