An electron enters a region where there is a magnetic field with a strength of 0.5 T which points out of the page (electron has an initial speed of 150 m/sec and is moving to the left). Describe motion of charge in an magnetic field (In particular, what is the shape of the path, what is its size, and what direction is it in?)
m•a = F
a = v^2/R is the normal (centripetal) acceleration,
F= q•v•B•sinα is Lorentz force , here, sinα = 1,
F =e•v•B,
e =1.6•10^-19 C is the charge of electrom,
m =9.1•10^-31 kg is the mass of electron.
m• v^2/R = e•v•B,
m• v/R = e•B,
R = m•v/e•B= =9.1•10^-31•150/1.6•10^-19•0.5= =1.71•10^-9 m.
The çath is the circle of ràdius
R = 1.71•10^-9 m.
If the electron moves to the left, and magnetic field points out of the page, the Lorentz force is directed downwards, therefore, the electron is rotating clockwise about the magnetic field lines.
Thanks Elena
The motion of a charged particle, such as an electron, in a magnetic field is influenced by the Lorentz force. The Lorentz force acts perpendicular to both the velocity of the charged particle and the magnetic field.
In this case, the electron is moving to the left, while the magnetic field points out of the page. According to the right-hand rule, the Lorentz force on the electron will be directed downwards. Therefore, the path of the electron will be curved or bent downwards.
The shape of the path that the electron follows is a circle. The radius of this circular path can be determined using the equation for the Lorentz force:
F = qvB
Where F is the applied force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field strength.
The Lorentz force provides the necessary centripetal force to keep the electron moving in a circular path. The centripetal force can be expressed as:
F = mv^2/r
Where m is the mass of the electron and r is the radius of the circular path.
Setting these two forces equal to each other, we can solve for the radius of the path:
qvB = mv^2/r
Simplifying, we find:
r = mv / (qB)
Plugging in the given values:
m = mass of an electron = 9.11 x 10^-31 kg
v = 150 m/s
q = charge of an electron = -1.6 x 10^-19 C
B = 0.5 T
r = (9.11 x 10^-31 kg) * (150 m/s) / (-1.6 x 10^-19 C * 0.5 T)
Calculating this, we can find the radius of the circular path that the electron will follow in this magnetic field.