An electron passes through two rectangular regions that contain uniform magnetic fields, B1 and B2. The field B1 is stronger than the field B2. Each field fills the region completely. How does the speed v1 of the electron in region 1 compare with the speed v2 in region 2?

v1 = v2

Explanation:

Given:

- The missing figure is (attached).

- The Magnetic Field B1 > B2

Find:

How does the speed v1 of the electron in region 1 compare with the speed v2 in region 2?

Solution:

- From Lorentz Law we know that the Force that acts on the charge particle is the cross product of Magnetic Field Vector ( B1 or B2 ) and the velocity vector (v1 or v1).

- From the attached figure related to this problem we see that the electron velocity or direction of motion is always parallel to the magnetic field B1&B2.

- The law of cross product for parallel vector is 0. Hence, the Lorentz force acting on the electron is also zero.

- Zero Force means no work is done on the particle by the magnetic field, thus, the change in kinetic energy also zero for conservation of energy to hold.

- The initial and final kinetic energies of the electron is same. Hence, we can conclude that v1 = v2.