Respuesta :
Answer:
(a). The speed of electron is [tex]1.56\times10^{7}\ m/s[/tex].
(b). The radius of electron is [tex]4.2\ cm[/tex]
Explanation:
Given that,
Length = 2.5 cm
Distance = 6.0 mm
Magnetic field = 2.1 T
Potential difference = 700 V
(a). We need to calculate the electron's speed
Using formula of speed
[tex]v=\sqrt{\dfrac{2eV}{m}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2\times1.6\times10^{-19}\times700}{9.1\times10^{-31}}}[/tex]
[tex]v=15689290.81\ m/s[/tex]
[tex]v=1.56\times10^{7}\ m/s[/tex]
(b). We need to calculate the radius of electron
Using formula of centripetal force
[tex]\dfrac{mv^2}{r}=qvB[/tex]
[tex]r=\dfrac{mv}{qB}[/tex]
Where,
m = mass of electron
v = speed of electron
r = radius
q = charge of electron
B = magnetic field
Put the value into the formula
[tex]r=\dfrac{9.1\times10^{-31}\times1.56\times10^{7}}{1.6\times10^{-19}\times2.1\times10^{-3}}[/tex]
[tex]r=0.042\ m[/tex]
[tex]r=4.2\ cm[/tex]
Hence, (a). The speed of electron is [tex]1.56\times10^{7}\ m/s[/tex].
(b). The radius of electron is 4.2 cm
