Magnetic Field and electric Field

[physicsdreams]

Homework Statement

A charged particle, passing through a certain region of space,has a velocity whose magnitude and directions remain constant.

a. If it is known that the external magnetic field is zeroseverywhere in this region, can you conclude that the external electric field is also zero? Explain.

b. If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field isalso zero? Explain.

The Attempt at a Solution

This is more of a conceptual question, and I really have no idea how to approach it.
If someone could help clarify this, that would be great!

Thanks

 

[Jolb]

Homework Statement

A charged particle, passing through a certain region of space,has a velocity whose magnitude and directions remain constant.

a. If it is known that the external magnetic field is zeroseverywhere in this region, can you conclude that the external electric field is also zero? Explain.

Well first of all I guess we have to assume that the particle doesn't experience any OTHER external forces, e.g. if it were confined to a wire or something. So from here on out I will assume the only forces possible are either electric or magnetic.

Suppose the electric field were nonzero. Then the charged particle would feel a force, and would thus experience some accelleration--i.e., its velocity's magnitude or direction would change.

b. If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field isalso zero? Explain.

This argument is slightly different. Remember the Lorentz force law : F = q(E+v x B). E is zero, so F = qv x B. Can this be zero for nonzero B?