Magnetic forces (no calculations)

[XxphysicsxX]

Problem:
An electron enters an external magnetic field in the same direction as the field. Explain what happens to motion of the electron while in the field.

I predicted the electron to stay still, since the angle between the direction of speed and external magnetic field is 0.

can anyone confirm or tell me if my answers wrong?
any extra detail would be greatly appreciated.

 

[jhae2.718]

You're correct. The force on the electron will be the Lorentz force, $\mathbf{F} = q[\mathbf{E} + \mathbf{v} \times \mathbf{B}]$.

Since there is nothing about it, it's reasonable to assume E=0. Then, what remains is $\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$. If $$\frac{\mathbf{B}}{B}=\frac{\mathbf{v}}{v}$$, then ${v} \times \mathbf{B}=vB\sin{\theta}=vB(0)=0 \Rightarrow \mathbf{F}=0$

So, if v₀ of the electron is zero, since no force acts upon it (considering the electron in isolation with only the magnetic field present), it should remain in place.

 

[XxphysicsxX]

thankyou!