Electron shot with initial velocity B field

In summary, an electron with an initial velocity of 3.5*10^6 is accelerated through a parallel plate capacitor with a potential difference of 70V. After traveling 5 mm on the x-axis, the total field produced by the electron, including electric and magnetic components, is 1.4 x 10^4 N/C + 2.3 x 10^-7 T in the x direction. This is calculated using the equations E= dv/dx and mag=mu/(4pi) (qv x r)/r^2.
  • #1
JonJon
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Homework Statement


Electron shot in x direction with V_o=3.5*10^6 and is accellerated thru parallel plate capacitor with potential difference of 70V. after it travels on the x-axis for 5 mm what is its total field the electron produces? including magnetic and electric. Show direction and magnitude


Homework Equations


E= dv/dx

E= 1/(4pi ep) *q/r^2

mag=mu/(4pi) (qv x r)/r^2


The Attempt at a Solution


E= 70/5x 10^-3 = 1.4 x 10^4
 
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  • #2
N/CE= 1/(4pi ep) *q/r^2 q=1.6 x 10^-19ep=8.85 x 10^-12r= 5x 10^-3E= 2.6 x 10^-2 N/C Magnetic field: mu=(4pi x 10^-7)qv= 1.6 x 10^-19 x 3.5 x 10^6mag= (4pi x 10^-7)/(4pi) (1.6 x 10^-19 x 3.5 x 10^6 x 5 x 10^-3)/(5 x 10^-3)^2mag=2.3 x 10^-7 Ttotal field vector = 1.4 x 10^4 N/C + 2.3 x 10^-7 T in x direction
 

1. What is an electron shot with initial velocity in a B field?

An electron shot with initial velocity in a B field refers to an experiment where an electron is launched or accelerated with a specific initial velocity in the presence of a magnetic field (B field). This experiment is often used to study the behavior of charged particles in magnetic fields.

2. How is the initial velocity of the electron determined?

The initial velocity of the electron is determined by the method of acceleration. This can be achieved using an electric field, such as in a cathode ray tube, or by using a particle accelerator. The initial velocity can also be calculated using equations that take into account the strength of the magnetic field and the mass of the electron.

3. What is the effect of the B field on the electron's trajectory?

The B field, or magnetic field, exerts a force on the moving electron, causing it to deflect from its original path. The strength and direction of the B field will determine the amount and direction of the deflection. This effect is used in many applications, such as in particle accelerators and MRI machines.

4. How does the initial velocity affect the path of the electron in a B field?

The initial velocity of the electron has a significant impact on its trajectory in a B field. A higher initial velocity will result in a larger deflection angle, while a lower initial velocity will result in a smaller deflection angle. This relationship can be described using the equations of motion and the Lorentz force law.

5. What are some real-world applications of studying electrons in B fields?

Studying electrons in B fields has a wide range of applications, including particle accelerators, MRI machines, and CRT televisions. It is also used in research to better understand the behavior of charged particles in magnetic fields, which has important implications in fields such as plasma physics and astronomy.

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