Question

1) A charged particle is fired into a cubical region of space where there is a uniform magnetic field. Outside this region, there is no magnetic field. Is it possible that particle will remain inside the cubical region? Why or why not?

2) A charged particle moves through a region of space with constant velocity (magnitude and direction). If the external magnetic field is zero in this region, can you conclude that the external field in the region is also zero? Explain. (By "external" we mean fields other than those produced by the charged particle) If the external electric field is zero in the region, can you conclude that the external magnetic field in the region is also zero?

Answer 1

(1)

If charge has V=const (V-speed)and Vis perpendicular to B (B magnetic field) then charge will move by circle trajectory rwhereV-speed m - mass of charg -charge B-magnetic field If r<G V2. (where -side of cubical regian) than charge won't come out from the cubical gion But if charge has V(Visn't perpendicular to B).then charge will move by spiral trajectory Charge will come out from the cubical region

(2) A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant.

(a) If it is known that the external magnetic field is zero everywhere in the region, we can conclude that the electric field is also zero. Any charged particle placed in an electric field will experience a force given by F = qE, where q is the charge and E is the electric field. If the magnitude and direction of the velocity of the particle are constant, then the particle has zero acceleration. From Newton's second law, we know that the net force on the particle is zero. But there is no magnetic field and, hence, no magnetic force. Therefore, the net force is the electric force. Since the electric force is zero, the electric field must be zero.

(b) If it is known that the external electric field is zero everywhere, we cannot conclude that the external magnetic field is also zero. In order for a moving charged particle to experience a magnetic force when it is placed in a magnetic field, the velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field. If the moving charged particle enters the region such that its velocity is parallel or antiparallel to the magnetic field, it will experience no magnetic force, even though a magnetic field is present. In the absence of an external electric field, there is no electric force either. Thus, there is no net force, and the velocity vector will not change in any way.