How do electric and magnetic fields affect the motion of an electron?

[brad sue]

Hi, I have this problem and I need some explanation and help to solve it:

An electron is injected at t=0sec with a velocity of v_o =(2*10^6 m/s) i into a region with parallel electric field E=(1500V/m)j and B=(-.2T)j,respectively.
Calculate the subsequent motion.

What I did is that I know that the motion will be a circular one.
then I computed R =m*v/(q*B)
Can I compute R this way since we have electric and magnetic fields together??

Also How can I find the acceleration? when I do V²/R I don't get the right answer at the back of the textbook.

Thank you
B

 

[gulsen]

Since there's an electric field, the magnitude of it's velocity increases, so the radii will chage. You can plug the Lorentz force into Newton's 2nd law.

 

[kyle8921]

obby

The presence of both electric and magnetic fields will indeed affect the motion of the electron. This is because charged particles, such as electrons, experience a force when they are in the presence of an electric or magnetic field. This force can cause the electron to accelerate or change direction.

In this scenario, the electron is injected with a velocity of 2*10^6 m/s in the direction of the electric field (j direction) and is also subject to a magnetic field in the same direction (j direction). This means that the electron will experience a force in both the electric and magnetic fields.

To calculate the subsequent motion, you can use the Lorentz force law, which states that the force on a charged particle in an electric and magnetic field is given by F = q(E + v x B). In this case, the force will be in the negative k direction (opposite to the direction of the electric and magnetic fields).

To find the acceleration, you can use the equation a = F/m, where m is the mass of the electron. This will give you the acceleration in the negative k direction.

To find the radius of the circular motion, you can use the equation R = mv/(qB), where m is the mass of the electron, v is the velocity, q is the charge of the electron, and B is the magnetic field strength. This equation is valid for charged particles moving in a magnetic field, regardless of the presence of an electric field.

It is important to note that the velocity and acceleration of the electron will change as it moves in the electric and magnetic fields. The initial velocity of 2*10^6 m/s will decrease due to the electric field, and the acceleration will also decrease as the electron's velocity increases.

I hope this helps to clarify how the electric and magnetic fields affect the motion of an electron and how you can calculate its subsequent motion. If you are still having trouble finding the correct answer, I suggest double-checking your calculations and units to ensure accuracy.