Answer:
The magnetic field is [tex]B = 8.21 *10^{-4} \ T[/tex]
The force is [tex]F= 3.599 *10^{-15} \ N[/tex]
Explanation:
From the question we are told that
The speed of the electron is [tex]v = 2.74 *10^{7} \ m/s[/tex]
The radius of the circular trajectory is [tex]r = 0.190 \ m[/tex]
Generally the magnetic force acting on the electron is equal to the centripetal acting on the the electron , this is is mathematically represented as
[tex]F_B = F_C[/tex]
Here [tex]F_B[/tex] is the magnetic force that will cause the electron to move in a circular path which is mathematically represented as
[tex]F_B = q * v * B sin(90)[/tex]
[tex]F_B = q * v * B[/tex]
while [tex]F_C[/tex] is the centripetal force which is mathematically represented as
[tex]F_C = \frac{m v^2}{r}[/tex]
=> [tex]q * v * B = \frac{m v^2}{r}[/tex]
=> [tex]B = \frac{m * v}{ q r }[/tex]
Here q is the charge on an electro with value [tex]q= 1.60 *10^{-19 } \ C[/tex]
and m is the mass of electron with value [tex]m = 9.11 *10^{-31} \ kg[/tex]
So
[tex]B = \frac{9.11 *10^{-31} * 2.74 *10^{7}}{ 1.60 *10^{-19} * 0.190 }[/tex]
=> [tex]B = 8.21 *10^{-4} \ T[/tex]
Generally when the magnetic field is [tex]B = 8.21 *10^{-4} \ T[/tex] the magnetic force is
[tex]F= q * B * v[/tex]
=> [tex]F= 1.60 *10^{-19} * 8.21 *10^{-4} * 2.74 *10^{7}[/tex]
=> [tex]F= 3.599 *10^{-15} \ N[/tex]
(a) The magnetic field will be B=8.21*10^-4 T
(b) The force is equal to F=3.599*10^-15 N
The magnetic filed is the influence of the magnetic force acts on a charged particle. The magnetic fields are generally generated by the flow of the currents.
From the question, it is given that
The speed of the electron is v=2.74*10^7 m/s
The radius of the circular trajectory is r=0.190 m
Generally the magnetic force acting on the electron is equal to the centripetal acting on the the electron , this is is mathematically represented as
[tex]F_B=F_C[/tex]
Here [tex]F_B[/tex] is the magnetic force that will cause the electron to move in a circular path which is mathematically represented as
[tex]F_B=q\times v\times Bsin(90)[/tex]
[tex]F_B=q\times v\times B[/tex]
while [tex]F_C[/tex] is the centripetal force, which is mathematically represented as
[tex]F_C=\dfrac{mv^2}{r}[/tex]
[tex]q\times v\times B=\dfrac{mv^2}{r}[/tex]
[tex]B=\dfrac{m\times v}{qr}[/tex]
Here q is the charge on an electron with value [tex]q=1.60\times 10^{-19} C[/tex]
and m is the mass of electron with value [tex]m=9.11\times 10^{-31} kg[/tex]
So
[tex]B= \dfrac{9.11\times 10^{-11}\times 2.74\times 10^7}{1.60\times 10^{-19}\times 0.190}[/tex]
[tex]B=8.21\times 10^{-4} \ T[/tex]
Generally when the magnetic field is the magnetic force is
[tex]F=q\times v\times B[/tex]
[tex]F=1.60\times 10^{-19}\times 8.21\times 10^{-4}\times 2.74\times 10^7[/tex]
[tex]F=3.599\times 10^{-15}\ N[/tex]
Thus the magnetic field will be B=8.21*10^-4 T and the force is equal to F=3.599*10^-15 N
To know more about Magnetic field follow
https://brainly.com/question/26257705
