Example 22.2 from College Physics, 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications

Calculating the Curvature of the Path of an Electron Moving in a Magnetic Field: A Magnet on a TV Screen

A magnet brought near an old-fashioned TV screen such as in Figure 22.21 (TV sets with cathode ray tubes instead of LCD screens) severely distorts its picture by altering the path of the electrons that make its phosphors glow. (Don’t try this at home, as it will permanently magnetize and ruin the TV.) To illustrate this, calculate the radius of curvature of the path of an electron having a velocity of $6 . 00 \times 10^{7} m/s$ (corresponding to the accelerating voltage of about 10.0 kV used in some TVs) perpendicular to a magnetic field of strength $B = 0 .500 T$ (obtainable with permanent magnets).

A bar magnet with the north pole set against the glass of a computer monitor. The magnetic field lines are shown running from the south pole through the magnet to the north pole. Paths of electrons that are emanating from the computer monitor are shown moving in straight lines until they encounter the magnetic field of the magnet. At that point, they change course and spiral around the magnetic field lines and toward the magnet.

Figure 22.21 Side view showing what happens when a magnet comes in contact with a computer monitor or TV screen. Electrons moving toward the screen spiral about magnetic field lines, maintaining the component of their velocity parallel to the field lines. This distorts the image on the screen.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We can find the radius of curvature $r$ directly from the equation $r = \frac{m v}{q B}$ , since all other quantities in it are given or known.
Solution
Using known values for the mass and charge of an electron, along with the given values of $v$ and $B$ gives us
$\begin{array}{l} r = \frac{mv}{qB} & = & \frac{(9 . 11 \times 10^{- 31} kg) (6 . 00 \times 10^{7} m/s)}{(1 . 60 \times 10^{- 19} C) (0.500 T)} \\ = & 6 . 83 \times 10^{- 4} m \end{array}$
22.8

or

$r = 0 . 683 mm .$
22.9
Discussion
The small radius indicates a large effect. The electrons in the TV picture tube are made to move in very tight circles, greatly altering their paths and distorting the image.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion

Strategy

Solution

Discussion