IB Physics SL D.3.2 Charge in magnetic fields

Practise predicting charged-particle motion in magnetic fields from force directions, circular-path equations and speed arguments.

Exam points

use qvB = mv^2/r to derive or calculate the radius, or read the gradient of an R-v graph correctly
use a page-based field diagram and curvature to identify the particle sign or possible particle type
state that speed stays constant because magnetic force is perpendicular to velocity, so no work is done

[Maximum number: 4]

(a)

A proton moves on a circular path in a region of uniform magnetic field of magnetic flux density B that is directed into the plane of the page.

[ 4 ]

(i)

On the diagram, draw an arrow to indicate the velocity of the proton at the position shown.

[ 1 ]

(ii)

Show that the frequency of revolution of the proton is given by $f=\frac{e B}{2 \pi m_{\mathrm{p}}}$ .

[ 3 ]

$\begin{aligned} e v B=\frac{m_{\mathrm{p}} v^{2}}{R} f=\frac{1}{T}=\frac{v}{2 \pi R} \end{aligned}$

Both q and e are acceptable for the
charge.

[3]

Algebra leading to required expression $\boldsymbol{<}=\frac{e B}{2 \pi m_{\mathrm{p}}} \boldsymbol{} \boldsymbol{}$

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D.3.2—Charge in magnetic fields question 1

Question (a)

Question (i)

Question (ii)