Given velocity and acceleration, determine magnetic field

[yanyin]

an electron has a velocity of 1.20 x 10^4 m/s(in the positive x direction), and an acceleration of 2.00 x 10^12 m/s^2 (in the positive z direction) in a uniform electric and magnetic field. if the electric field has magnitude of 20.0N/C (in the positive z direction), what can you determine about the magnetic field in the region? what can you not determine?
(Please show steps and why, the correct answers i got are Bx(any value), By = -2.6mT, Bz=0)

 

[GRQC]

Originally posted by yanyin
an electron has a velocity of 1.20 x 10^4 m/s(in the positive x direction), and an acceleration of 2.00 x 10^12 m/s^2 (in the positive z direction) in a uniform electric and magnetic field. if the electric field has magnitude of 20.0N/C (in the positive z direction), what can you determine about the magnetic field in the region? what can you not determine?
(Please show steps and why, the correct answers i got are Bx(any value), By = -2.6mT, Bz=0)

Do we get the credit instead of you if we answer your homework/take-home exam question?

 

[Graeme Robinson]

To determine the magnetic field in the region, we can use the equation F=qE+q(vxB). In this equation, F represents the net force on the electron, q is the charge of the electron, E is the electric field, v is the velocity of the electron, and B is the magnetic field.

First, we need to find the net force on the electron. We can use the equation F=ma, where m is the mass of the electron and a is the acceleration. Plugging in the values given, we get F= (9.11 x 10^-31 kg)(2.00 x 10^12 m/s^2) = 1.82 x 10^-18 N.

Next, we can use the equation F=qE+q(vxB) and solve for B. Since the electron is moving in the positive x direction, the cross product vxB will be in the positive y direction. Plugging in the values, we get:

1.82 x 10^-18 N = (1.60 x 10^-19 C)(20.0 N/C) + (1.60 x 10^-19 C)(1.20 x 10^4 m/s)(B)

Simplifying, we get B = -2.6 x 10^-5 T in the positive y direction.

This means that the magnetic field in the region is 2.6 x 10^-5 T in the negative y direction. However, we cannot determine the values for the magnetic field in the x and z directions. This is because the electron is only experiencing a force in the y direction due to the combination of the electric and magnetic fields. Without any additional information about the electron's motion in the x and z directions, we cannot determine the magnetic field in those directions. Therefore, Bx can have any value and Bz is equal to 0.