Back to Exercise: Magnetic Fields, Field Lines, and Force

Exercises: Magnetic Fields, Field Lines, and Force

Work through each section in order. Show your work where indicated. For direction problems, state your answer as a cardinal direction (up, down, left, right, into page, out of page) or compass direction as appropriate.

Grade 11·22 problems·~30 min·OpenStax Physics (High School)·section·sec-20-1

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Recall / Warm-Up

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

Electric fields are created by stationary or moving charges; magnetic fields are created only by moving charges.

Electric fields and magnetic fields are identical — they are just different names for the same phenomenon.

Magnetic fields are created by stationary charges; electric fields require moving charges.

Both fields exert forces in the same direction on a positive charge.

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

A permanent bar magnet

A stationary point charge

A current-carrying wire

Earth's liquid iron core

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.

Field lines must emerge from the north pole and enter the south pole.

Field lines must never cross.

Field lines must form closed loops.

Field line density must be greater near the poles.

Fluency Practice

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?

$1\ \text{T} = 1\ \frac{\text{kg}}{\text{A} \cdot \text{s}^2}$

$1\ \text{T} = 1\ \frac{\text{N}}{\text{C}}$

$1\ \text{T} = 1\ \frac{\text{V}}{\text{m}}$

$1\ \text{T} = 1\ \frac{\text{J}}{\text{C} \cdot \text{m}}$

3D coordinate system showing velocity v pointing right along x-axis, magnetic field B pointing up along y-axis, with the force direction to be determined using the right-hand rule

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?

Out of the page (in the $+z$ direction)

Into the page (in the $-z$ direction)

Upward (in the $+y$ direction)

Downward (in the $-y$ direction)

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?

Upward ( $+y$ )

Into the page ( $-z$ )

Out of the page ( $+z$ )

To the right ( $+x$ )

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.

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