 # An electron originates at a point A lying on the axis of a straight solenoid and moves with velocity v at an angle `y` to the axis. The magnetic induction of the field is equal to B. A screen is oreinted at right angles to the axis and is located at a distance l from the point A. Find the distance from the axis to the point on the screen into which he electron strikes?

12 years ago

Dear student,

F
=
q

v
X
B

F
=
q

v
X
B

1: There is no magnetic force on a stationary charge (v=0). As such, our study here refers to situations in which charge is moving with certain velocity in the magnetic field. This condition is met when the charge is released with certian velocity in the magnetic field.

2: The magnetic field (B) is an uniform stationary magnetic field for our consideration in the module. It means that the magnitude and direction of magnetic field do not change during motion. The charged particle, however, is subjected to magnetic force acting side way. The direction of motion of charged particle, therefore, changes. In turn, the direction of magnetic force being perpendicular to velocity also changes. Important point to underline here is that this loop of changing directions of velocity and magnetic force is continuous. In other words, the directions of both velocity and magnetic force keeps changing continuously with the progress of motion.

This aspect of continuous change is shown in the figure below. Note that direction of magnetic field is fixed in y-direction. Initially, the charged particle is at the origin of coordinate reference with a velocity v in x-direction. Applying right hand rule for vector cross product and considering a point positive charge, we see that magnetic force is directed in z-direction. As a result, the particle is drawn to move along a curved path with velocity (having same speed) directed tangential to it. The magnetic force vector also changes sign being perpendicular to velocity vector. In this manner, we see that the directions of both velocity and magnetic force keeps changing continuously as pointed out.

All the best.

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