Magnetic Forces and Fields — Practice Quiz

A Physics cheat sheet for Magnetic Forces and Fields — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Magnetic Force on Charge: Force \(F\) on charge \(q\) moving with speed \(v\) in magnetic field \(B\) at angle \(\theta\).

$$F = |q|vB \sin \theta$$

Circular Path Radius: Radius \(r\) of path for charge \(q\) with mass \(m\) moving perpendicular to magnetic field \(B\).

$$r = \frac{mv}{|q|B}$$

Magnetic Force on Wire: Force \(F\) on wire of length \(L\) carrying current \(I\) in magnetic field \(B\) at angle \(\theta\).

$$F = ILB \sin \theta$$

Torque on Coil: Torque \(\tau\) on coil with \(N\) turns, area \(A\), current \(I\) in field \(B\). \(\phi\) is angle between normal and field.

$$\tau = NIAB \sin \phi$$

Magnetic Field of Long Wire: Field \(B\) at distance \(r\) from long straight wire carrying current \(I\).

$$B = \frac{\mu_0 I}{2 \pi r}$$

Where: \(\mu_0\) = permeability of free space \((4\pi \times 10^{-7} T\cdot m/A)\)

Magnetic Field of Loop Center: Field \(B\) at center of circular loop of radius \(R\) with \(N\) turns.

$$B = \frac{N \mu_0 I}{2 R}$$

Magnetic Field of Solenoid: Field \(B\) inside solenoid with \(n\) turns per unit length.

$$B = \mu_0 n I$$

Ampere's Law: Line integral of magnetic field around a closed loop equals \(\mu_0\) times enclosed current.

$$\Sigma B_{\parallel} \Delta \ell = \mu_0 I$$

Practice quiz

  1. An electron moves at a speed of $2 \times 10^6 \text{ m/s}$ perpendicular to a uniform magnetic field of $0.5 \text{ T}$. What is the magnitude of the magnetic force on the electron? (Charge of electron is $1.6 \times 10^{-19} \text{ C}$)

    • $1.6 \times 10^{-13} \text{ N}$
    • $8.0 \times 10^{-14} \text{ N}$
    • $3.2 \times 10^{-13} \text{ N}$
    • $0 \text{ N}$

    Answer: $1.6 \times 10^{-13} \text{ N}$

  2. A proton (mass $1.67 \times 10^{-27} \text{ kg}$, charge $1.6 \times 10^{-19} \text{ C}$) moves at $3 \times 10^5 \text{ m/s}$ perpendicular to a $0.2 \text{ T}$ magnetic field. What is the radius of its circular path?

    • $1.56 \times 10^{-2} \text{ m}$
    • $3.12 \times 10^{-2} \text{ m}$
    • $7.80 \times 10^{-3} \text{ m}$
    • $6.24 \times 10^{-2} \text{ m}$

    Answer: $1.56 \times 10^{-2} \text{ m}$

  3. A $0.2 \text{ m}$ long wire carrying a current of $5 \text{ A}$ is placed in a uniform magnetic field of $0.8 \text{ T}$. If the wire makes an angle of $30^\circ$ with the magnetic field, what is the magnitude of the magnetic force on the wire?

    • $0.4 \text{ N}$
    • $0.8 \text{ N}$
    • $0.2 \text{ N}$
    • $0.1 \text{ N}$

    Answer: $0.4 \text{ N}$

  4. A circular coil with $100$ turns and an area of $0.01 \text{ m}^2$ carries a current of $2 \text{ A}$. It is placed in a uniform magnetic field of $0.5 \text{ T}$. If the normal to the coil's plane makes an angle of $60^\circ$ with the magnetic field, what is the magnitude of the torque on the coil?

    • $0.866 \text{ N} \cdot \text{m}$
    • $1.00 \text{ N} \cdot \text{m}$
    • $0.500 \text{ N} \cdot \text{m}$
    • $1.732 \text{ N} \cdot \text{m}$

    Answer: $0.866 \text{ N} \cdot \text{m}$

  5. What is the magnitude of the magnetic field at a distance of $5 \text{ cm}$ from a long straight wire carrying a current of $10 \text{ A}$? (Use $\mu_0 = 4\pi \times 10^{-7} \text{ T} \cdot \text{m/A}$)

    • $4 \times 10^{-5} \text{ T}$
    • $2 \times 10^{-5} \text{ T}$
    • $8 \times 10^{-5} \text{ T}$
    • $1 \times 10^{-4} \text{ T}$

    Answer: $4 \times 10^{-5} \text{ T}$

  6. A single circular loop of wire with a radius of $10 \text{ cm}$ carries a current of $3 \text{ A}$. What is the magnetic field strength at the center of the loop? (Use $\mu_0 = 4\pi \times 10^{-7} \text{ T} \cdot \text{m/A}$)

    • $1.88 \times 10^{-5} \text{ T}$
    • $3.77 \times 10^{-5} \text{ T}$
    • $9.42 \times 10^{-6} \text{ T}$
    • $6.00 \times 10^{-6} \text{ T}$

    Answer: $1.88 \times 10^{-5} \text{ T}$

  7. A solenoid has $500$ turns per meter and carries a current of $0.5 \text{ A}$. What is the magnetic field strength inside the solenoid? (Use $\mu_0 = 4\pi \times 10^{-7} \text{ T} \cdot \text{m/A}$)

    • $3.14 \times 10^{-4} \text{ T}$
    • $6.28 \times 10^{-4} \text{ T}$
    • $1.57 \times 10^{-4} \text{ T}$
    • $1.00 \times 10^{-4} \text{ T}$

    Answer: $3.14 \times 10^{-4} \text{ T}$

  8. Ampere's Law, $\Sigma B_{\parallel} \Delta \ell = \mu_0 I$, relates the line integral of the magnetic field around a closed loop to which quantity?

    • The total current enclosed by the loop.
    • The magnetic flux through the loop.
    • The magnetic field strength at the center of the loop.
    • The magnetic force on a charge moving within the loop.

    Answer: The total current enclosed by the loop.

  9. Under what condition will a charged particle moving in a uniform magnetic field experience zero magnetic force?

    • When its velocity is perpendicular to the magnetic field.
    • When its velocity is parallel or anti-parallel to the magnetic field.
    • When the magnetic field strength is very high.
    • When the particle's charge is very large.

    Answer: When its velocity is parallel or anti-parallel to the magnetic field.

  10. A long straight wire and a circular loop both carry the same current $I$. If you measure the magnetic field at a distance $r$ from the straight wire and at the center of the loop with radius $R=r$, how do the magnitudes of the magnetic fields compare?

    • The magnetic field at the center of the loop is greater than that of the straight wire.
    • The magnetic field of the straight wire is greater than that at the center of the loop.
    • The magnetic fields are equal in magnitude.
    • The comparison depends on the specific value of current $I$.

    Answer: The magnetic field at the center of the loop is greater than that of the straight wire.

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