Fyneman exercise II ch1-4

Q.

In a certain region of space, there is a uniform electric field $\vec{E}$ of 10,000 volts per centimeter in the $+x$ direction. There is in the same region a uniform magnetic filed $\vec{B}$ in the $+y$ direction. A beam of mu-measons with the velocity ${c \over 3}$ travels through this region on a straight line in the $+z$ direction.

a)

What is the strength of the field $\vec{B}$? (A mu-meason has a mass 210 times the electron mass and a charge equal in magnitude to the electron charge.)

b)

Can you tell from this experiment if the charge on the measons is + or -?

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Trial.

Electromagnetic force
$\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})\tag{1}$

a)

$\vec{E}=10^6\hat{e}_x\ \ V\cdot m^{-1}$
$\vec{v}=c\hat{e}_z=3.00\times 10^8\hat{e}_z\ \ m\cdot s^{-2}$

From eq.(1), force is
$\vec{F}=q(10^6\hat{e}_x-3.00\times 10^8 B_y\hat{e}_x)$.

Problem said muons move on a straight line with velocity ${c \over 3}$, which means no external force, $\vec{F}=0$.

$B_y = {10^6 \over 3.00 \times 10^8}=3.33\times 10^{-3}$

$\therefore \vec{B}=3.33\times 10^{-3}\hat{e}_y$

b)

I can’t tell muon is + or - charge only with this experiment.